{"id":685,"date":"2024-02-15T10:12:57","date_gmt":"2024-02-15T02:12:57","guid":{"rendered":"https:\/\/big-tan.top\/?p=685"},"modified":"2024-02-15T11:55:33","modified_gmt":"2024-02-15T03:55:33","slug":"%e4%b8%96%e7%95%8c%e5%90%84%e5%9b%bd%e4%b8%ad%e5%ad%a6%e6%95%b0%e5%ad%a6%e7%ab%9e%e8%b5%9b%e9%a2%98%e9%9b%86%e9%94%a6%ef%bc%88%e4%ba%8c%ef%bc%89","status":"publish","type":"post","link":"https:\/\/itantan.eu.org\/?p=685","title":{"rendered":"\u4e16\u754c\u5404\u56fd\u4e2d\u5b66\u6570\u5b66\u7ade\u8d5b\u9898\u96c6\u9526\uff08\u4e8c\uff09"},"content":{"rendered":"\n<div class=\"wp-block-stackable-columns stk-block-columns stk-block stk-30ab688 stk-block-background\" data-block-id=\"30ab688\"><style>.stk-30ab688{background-color:#F6F6F6 !important;border-top-left-radius:18px !important;border-top-right-radius:18px !important;border-bottom-right-radius:18px !important;border-bottom-left-radius:18px !important;border-style:solid !important;margin-bottom:0px !important;overflow:auto !important}.stk-30ab688:before{background-color:#F6F6F6 !important}<\/style><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-30ab688-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-26cebeb\" data-v=\"4\" data-block-id=\"26cebeb\"><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-26cebeb-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-26cebeb-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-74de5a2\" data-block-id=\"74de5a2\"><p class=\"stk-block-text__text\">\u2003\u2003<strong>\u9898\u76ee\u4e00\uff1a\u4e2d\u56fd\u53f0\u6e7e\u521d\u4e2d\u6570\u5b66\u7ade\u8d5b\u9898\u76ee\uff0c\u82e5$a+b=12$\uff0c\u6c42$\\sqrt{a^2+4}+\\sqrt{b^2+49}$\u7684\u6700\u5c0f\u503c\u3002<\/strong><br>\u2003\u2003<strong>\u89e3\u9898\u601d\u8def\uff1a<\/strong>\u7c7b\u4f3c\u9898\u76ee\uff0c\u5982\u679c\u4ee3\u5165\u6c42\u53d6\u6700\u5c0f\u503c\uff0c\u96be\u5ea6\u8f83\u5927\uff0c\u53ef\u4ee5\u6362\u4e00\u79cd\u601d\u7ef4\u65b9\u5f0f\uff0c\u7528\u6570\u5f62\u7ed3\u5408\u7684\u65b9\u6cd5\u6c42\u89e3\uff0c\u4e0d\u4ec5\u5bb9\u6613\u7406\u89e3\u800c\u4e14\u7b80\u6d01\u660e\u4e86\u3002<\/p><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-stackable-columns stk-block-columns stk-block stk-a7d12b5 stk-block-background\" data-block-id=\"a7d12b5\"><style>.stk-a7d12b5{background-color:#F6F6F6 !important;border-top-left-radius:18px !important;border-top-right-radius:18px !important;border-bottom-right-radius:18px !important;border-bottom-left-radius:18px !important;border-style:solid !important;margin-bottom:0px !important;overflow:auto !important}.stk-a7d12b5:before{background-color:#F6F6F6 !important}<\/style><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-a7d12b5-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-6588b7c\" data-v=\"4\" data-block-id=\"6588b7c\"><style>@media screen and (min-width:768px){.stk-6588b7c{flex:1 1 calc(41.7% - var(--stk-column-gap,0px) * 1 \/ 2 ) !important}}<\/style><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-6588b7c-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-6588b7c-inner-blocks\">\n<div class=\"wp-block-stackable-image stk-block-image stk-block stk-24006a7\" data-block-id=\"24006a7\"><style>.stk-24006a7{overflow:auto !important}.stk-24006a7 .stk-img-wrapper{width:75% !important;height:200px !important}<\/style><figure><span class=\"stk-img-wrapper stk-image--shape-stretch\"><img loading=\"lazy\" decoding=\"async\" class=\"stk-img wp-image-689\" src=\"https:\/\/itantan.eu.org\/wp-content\/uploads\/2024\/02\/geogebra-\u5404\u56fd\u7ade\u8d5b-02-01.png\" width=\"920\" height=\"660\" srcset=\"https:\/\/itantan.eu.org\/wp-content\/uploads\/2024\/02\/geogebra-\u5404\u56fd\u7ade\u8d5b-02-01.png 920w, https:\/\/itantan.eu.org\/wp-content\/uploads\/2024\/02\/geogebra-\u5404\u56fd\u7ade\u8d5b-02-01-300x215.png 300w, https:\/\/itantan.eu.org\/wp-content\/uploads\/2024\/02\/geogebra-\u5404\u56fd\u7ade\u8d5b-02-01-768x551.png 768w\" sizes=\"auto, (max-width: 920px) 100vw, 920px\" \/><\/span><\/figure><\/div>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-9a80550\" data-v=\"4\" data-block-id=\"9a80550\"><style>@media screen and (min-width:768px){.stk-9a80550{flex:1 1 calc(58.29999999999998% - var(--stk-column-gap,0px) * 1 \/ 2 ) !important}}<\/style><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-9a80550-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-9a80550-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-13e3f31\" data-block-id=\"13e3f31\"><style>.stk-13e3f31{overflow:auto !important}<\/style><p class=\"stk-block-text__text\">\u7ebf\u6bb5$AB=12\uff0cAF=a\uff0cBF=b$\uff0c\u8fc7B\u70b9\u4f5cAB\u7684\u5782\u76f4\u7ebf\u6bb5$BC=7$\uff0c\u8fc7A\u70b9\u4f5cAB\u7684\u5782\u76f4\u7ebf\u6bb5AD=2\uff0c\u8fde\u63a5CF\u3001DF\uff0c\u5219$\\triangle CBF\u548c\\triangle DAF$\u90fd\u662f\u76f4\u89d2\u4e09\u89d2\u5f62\uff0c\u6839\u636e\u52fe\u80a1\u5b9a\u7406\u53ef\u5f97\uff1a$CF=\\sqrt{b^2+7^2}\uff0cDF=\\sqrt{a^2+2^2}$\uff0c\u4e24\u70b9\u4e4b\u95f4\u7ebf\u6bb5\u6700\u77ed\uff01\u663e\u7136\u5f53\u7ebf\u6bb5CF\u3001DF\u5728\u540c\u4e00\u6761\u76f4\u7ebf\u4e0a\u65f6CD\u7684\u503c\u662f\u6700\u5c0f\u7684\u3002\u8fc7D\u70b9\u4f5cAB\u7684\u5e73\u884c\u7ebf\uff0c\u4e0eBC\u5ef6\u957f\u7ebf\u4ea4\u4e8eE\u70b9\u3002<\/p><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-stackable-columns stk-block-columns stk-block stk-d5a9fa0 stk-block-background\" data-block-id=\"d5a9fa0\"><style>.stk-d5a9fa0{background-color:#F6F6F6 !important;border-top-left-radius:18px !important;border-top-right-radius:18px !important;border-bottom-right-radius:18px !important;border-bottom-left-radius:18px !important;border-style:solid !important;overflow:auto !important}.stk-d5a9fa0:before{background-color:#F6F6F6 !important}<\/style><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-d5a9fa0-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-6eba5c6\" data-v=\"4\" data-block-id=\"6eba5c6\"><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-6eba5c6-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-6eba5c6-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-8f23ebe\" data-block-id=\"8f23ebe\"><p class=\"stk-block-text__text\">$\\begin{split}\\text{\u89e3\uff1a}\\\\&amp;\\because a+b=12\\Rightarrow AB=DE=12\uff0cCE=BC+BE=9\\\\&amp;\\therefore\\text{\u6839\u636e\u52fe\u80a1\u5b9a\u7406\u53ef\u5f97\uff1a}(CD)^2=(CE)^2+(DE)^2\\\\&amp;\\therefore CD=\\sqrt{a^2+2^2}+\\sqrt{b^2+7^2}=\\sqrt{(CE)^2+(DE)^2}=\\sqrt{{12}^2+9^2}=15\\\\\\\\&amp;\\therefore\\text{\u6570\u5f62\u7ed3\u5408\u6709\u7684\u65f6\u5019\u662f\u89e3\u51b3\u4ee3\u6570\u5f0f\u6700\u5927\u503c\u3001\u6700\u5c0f\u503c\u95ee\u9898\u7684\u6cd5\u5b9d\uff0c\u7b80\u6d01\u660e\u4e86\uff0c\u5c24\u5176\u9002\u5408\u586b\u7a7a\u9898\u548c\u9009\u62e9\u9898\uff01}\\end{split}$<\/p><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-stackable-columns stk-block-columns stk-block stk-00c1a23 stk-block-background\" data-block-id=\"00c1a23\"><style>.stk-00c1a23{background-color:#ffe2c7 !important;border-top-left-radius:18px !important;border-top-right-radius:18px !important;border-bottom-right-radius:18px !important;border-bottom-left-radius:18px !important;border-style:solid !important;margin-bottom:0px !important;overflow:auto !important}.stk-00c1a23:before{background-color:#ffe2c7 !important}<\/style><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-00c1a23-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-84f00aa\" data-v=\"4\" data-block-id=\"84f00aa\"><style>.stk-84f00aa{overflow:auto !important}@media screen and (min-width:768px){.stk-84f00aa{flex:1 1 calc(55.19999999999999% - var(--stk-column-gap,0px) * 1 \/ 2 ) !important}}<\/style><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-84f00aa-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-84f00aa-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-70afb5d\" data-block-id=\"70afb5d\"><p class=\"stk-block-text__text\">\u2003\u2003<strong>\u9898\u76ee\u4e8c\uff1a$\\begin{split}&amp;\\triangle ABC\u4e2d\uff0cAB=CD\uff0c\\\\&amp;\\angle ABD=40^{\\circ}\uff0c\\angle BAD=30^{\\circ}\uff0c\\end{split}$\u6c42$\\angle\\alpha=\\angle ACD=?$\uff0c\u5965\u6570\u7ade\u8d5b\u51e0\u4f55\u9898\u76ee\uff0c\u5982\u679c\u6ca1\u6709\u60f3\u5230\u5de7\u5999\u7684\u8f85\u52a9\u7ebf\uff0c\u505a\u8d77\u6765\u6bd4\u8f83\u96be\u3002<\/strong><\/p><\/div>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-c76df16\" data-v=\"4\" data-block-id=\"c76df16\"><style>@media screen and (min-width:768px){.stk-c76df16{flex:1 1 calc(44.8% - var(--stk-column-gap,0px) * 1 \/ 2 ) !important}}<\/style><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-c76df16-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-c76df16-inner-blocks\">\n<div class=\"wp-block-stackable-image stk-block-image stk-block stk-96bd659\" data-block-id=\"96bd659\"><style>.stk-96bd659{overflow:auto !important}.stk-96bd659 .stk-img-wrapper{width:100% !important;height:172px !important}<\/style><figure><span class=\"stk-img-wrapper stk-image--shape-stretch\"><img loading=\"lazy\" decoding=\"async\" class=\"stk-img wp-image-691\" src=\"https:\/\/itantan.eu.org\/wp-content\/uploads\/2024\/02\/geogebra-\u5404\u56fd\u7ade\u8d5b-02-02-1.png\" width=\"1400\" height=\"800\" srcset=\"https:\/\/itantan.eu.org\/wp-content\/uploads\/2024\/02\/geogebra-\u5404\u56fd\u7ade\u8d5b-02-02-1.png 1400w, https:\/\/itantan.eu.org\/wp-content\/uploads\/2024\/02\/geogebra-\u5404\u56fd\u7ade\u8d5b-02-02-1-300x171.png 300w, https:\/\/itantan.eu.org\/wp-content\/uploads\/2024\/02\/geogebra-\u5404\u56fd\u7ade\u8d5b-02-02-1-1024x585.png 1024w, https:\/\/itantan.eu.org\/wp-content\/uploads\/2024\/02\/geogebra-\u5404\u56fd\u7ade\u8d5b-02-02-1-768x439.png 768w\" sizes=\"auto, (max-width: 1400px) 100vw, 1400px\" \/><\/span><\/figure><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-stackable-columns stk-block-columns stk-block stk-2a68e03 stk-block-background\" data-block-id=\"2a68e03\"><style>.stk-2a68e03{background-color:#ffe2c7 !important;border-top-left-radius:18px !important;border-top-right-radius:18px !important;border-bottom-right-radius:18px !important;border-bottom-left-radius:18px !important;border-style:solid !important;overflow:auto !important}.stk-2a68e03:before{background-color:#ffe2c7 !important}<\/style><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-2a68e03-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-b15a15e\" data-v=\"4\" data-block-id=\"b15a15e\"><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-b15a15e-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-b15a15e-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-4c7eb2e\" data-block-id=\"4c7eb2e\"><p class=\"stk-block-text__text\">$\\begin{split}\\text{\u89e3\uff1a}\\\\&amp;\u4f5c\u8f85\u52a9\u7ebf\uff0c\u5728BC\u4e0a\u53d6\u4e00\u70b9E\uff0c\u8fde\u63a5AE\uff0c\u4f7f\u5f97:BA=BE\uff0c\\triangle ABE\u662f\u7b49\u8170\u4e09\u89d2\u5f62\\\\&amp;\\therefore AB=BE\uff0c\\angle AED=70^{\\circ}\uff0c\\angle DAE=40^{\\circ}\\Rightarrow \\angle ADE=70^{\\circ}\uff0c\\triangle ADE\u4e5f\u662f\u7b49\u8170\u4e09\u89d2\u5f62\\\\&amp;\\Rightarrow AE=AD\\\\&amp;\\because AB=BE=CD\\\\&amp;\\therefore BD=BE-DE=AB-DE=CD-DE=CE\\\\&amp;\\Rightarrow BD=CE\uff0c\\angle ADB=\\angle AEC=180^{\\circ}-70^{\\circ}=110^{\\circ}\\\\&amp;\\therefore \\triangle ABD\\cong\\triangle ACE\\\\&amp;\\therefore \\angle\\alpha=\\angle ACE=\\angle ABD=40^{\\circ}\\end{split}$<\/p><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-stackable-columns stk-block-columns stk-block stk-bd9ab15 stk-block-background\" data-block-id=\"bd9ab15\"><style>.stk-bd9ab15{background-color:#F6F6F6 !important;border-top-left-radius:18px !important;border-top-right-radius:18px !important;border-bottom-right-radius:18px !important;border-bottom-left-radius:18px !important;border-style:solid !important;margin-bottom:0px !important;overflow:auto !important}.stk-bd9ab15:before{background-color:#F6F6F6 !important}<\/style><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-bd9ab15-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-42ef1f5\" data-v=\"4\" data-block-id=\"42ef1f5\"><style>@media screen and (min-width:768px){.stk-42ef1f5{flex:1 1 calc(61.79999999999998% - var(--stk-column-gap,0px) * 1 \/ 2 ) !important}}<\/style><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-42ef1f5-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-42ef1f5-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-cdc4c77\" data-block-id=\"cdc4c77\"><style>.stk-cdc4c77{overflow:auto !important}<\/style><p class=\"stk-block-text__text\">\u2003\u2003<strong>\u62d3\u5c55\u601d\u7ef4\u9898\uff1a\u4fc4\u7f57\u65af\u7684\u521d\u4e2d\u6570\u5b66\u7ade\u8d5b\u9898\u76ee\uff0c\u6709\u4e9b\u731b\u3002\u6c42\uff1a$\\bbox[yellow,5pt,border:2px solid red]{\\cos18^{\\circ}\\sin36^{\\circ}}$\u7684\u503c\u3002<\/strong><br>\u2003\u2003<strong>\u89e3\u9898\u601d\u8def\uff1a<\/strong>$\\sin18^{\\circ}$\u7684\u503c\u53ef\u4ee5\u4f7f\u7528\u6570\u5f62\u7ed3\u5408\u7684\u65b9\u5f0f\u6c42\u89e3\uff0c\u65e2\u7136$\\sin18^{\\circ}$\u53ef\u4ee5\u6c42\u89e3\uff0c\u90a3\u4e48$\\cos18^{\\circ}$\u4e5f\u53ef\u4ee5\u6c42\u89e3\u3002\u540c\u6837\uff0c$\\sin36^{\\circ}$\u4e5f\u53ef\u4ee5\u7528\u6570\u578b\u7ed3\u5408\u7684\u65b9\u5f0f\u8fdb\u884c\u8ba1\u7b97\u3002\u603b\u4e4b\uff0c\u5982\u679c\u53ea\u7528\u521d\u4e2d\u77e5\u8bc6\u6c42\u89e3\uff0c\u8ba1\u7b97\u91cf\u8f83\u5927\uff0c\u5316\u7b80\u8d77\u6765\u9700\u8981\u4e00\u5b9a\u7684\u53d8\u6362\u6280\u5de7\uff0c\u8fd9\u4e2a$\\sin18^{\\circ}$\u7684\u6c42\u503c\u65b9\u6cd5\u5728\u521d\u4e2d\u6570\u5b66\u7ade\u8d5b\u4e2d\u5e38\u89c1\uff0c\u4e00\u822c\u6765\u8bf4\uff0c\u5c31\u662f\u6570\u5f62\u7ed3\u5408\u6c42\u503c\u6700\u7b80\u6d01\u3002<\/p><\/div>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-3e8ea40\" data-v=\"4\" data-block-id=\"3e8ea40\"><style>@media screen and (min-width:768px){.stk-3e8ea40{flex:1 1 calc(38.2% - var(--stk-column-gap,0px) * 1 \/ 2 ) !important}}<\/style><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-3e8ea40-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-3e8ea40-inner-blocks\">\n<div class=\"wp-block-stackable-image stk-block-image stk-block stk-573653d\" data-block-id=\"573653d\"><style>.stk-573653d{overflow:auto !important}.stk-573653d .stk-img-wrapper{width:63% !important;height:250px !important}<\/style><figure><span class=\"stk-img-wrapper stk-image--shape-stretch\"><img loading=\"lazy\" decoding=\"async\" class=\"stk-img wp-image-688\" src=\"https:\/\/itantan.eu.org\/wp-content\/uploads\/2024\/02\/geogebra-JingSai-2-07-ABC.png\" width=\"700\" height=\"860\" srcset=\"https:\/\/itantan.eu.org\/wp-content\/uploads\/2024\/02\/geogebra-JingSai-2-07-ABC.png 700w, https:\/\/itantan.eu.org\/wp-content\/uploads\/2024\/02\/geogebra-JingSai-2-07-ABC-244x300.png 244w\" sizes=\"auto, (max-width: 700px) 100vw, 700px\" \/><\/span><\/figure><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-stackable-columns stk-block-columns stk-block stk-e8858ff stk-block-background\" data-block-id=\"e8858ff\"><style>.stk-e8858ff{background-color:#F6F6F6 !important;border-top-left-radius:18px !important;border-top-right-radius:18px !important;border-bottom-right-radius:18px !important;border-bottom-left-radius:18px !important;border-style:solid !important;overflow:auto !important}.stk-e8858ff:before{background-color:#F6F6F6 !important}<\/style><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-e8858ff-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-044d5d0\" data-v=\"4\" data-block-id=\"044d5d0\"><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-044d5d0-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-044d5d0-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-0b30439\" data-block-id=\"0b30439\"><p class=\"stk-block-text__text\">$\\begin{split}\\text{\u89e3\uff1a}\\\\&amp;\u521d\u4e2d\u89e3\u6cd5\uff1a\u4f5c\u4e00\u4e2a\u7b49\u8170\u4e09\u89d2\u5f62\\triangle ABC\uff0c\u9876\u89d2\u4e3a\\angle BAC=36^{\\circ}\uff0c\u4e24\u4e2a\u5e95\u89d2\u4e3a\\angle ABC=\\angle ACB=72^{\\circ}\uff1b\\\\&amp;\u8fc7B\u70b9\u4f5c\\angle ABC\u7684\u89d2\u5e73\u5206\u7ebf\u4ea4\u8fb9AC\u4e8eD\u70b9\uff0c\u8fc7A\u70b9\u4f5c\u5e95\u8fb9AC\u7684\u9ad8\u4ea4\u4e8eE\u70b9\u3002\\\\&amp;\u8fc7B\u70b9\u4f5c\u8fb9AC\u7684\u9ad8\u4ea4\u4e8eF\u70b9\\\\&amp;\\therefore \\triangle DAB\u548c \\triangle BCD\u4e5f\u662f\u7b49\u8170\u4e09\u89d2\u5f62\uff1a\u8bbeAD=BD=BC=1\uff0cDC=m\\\\&amp;\\because \\triangle ABC\\backsim\\triangle BCD\\Rightarrow \\dfrac{AC}{BC}=\\dfrac{BC}{DC}=\\dfrac{BD}{DC}\\Rightarrow \\dfrac{1+m}{1}=\\dfrac{1}{m}\\\\&amp;\\therefore m^2+m-1=0\\Rightarrow m=\\dfrac{-1\\pm\\sqrt5}{2}\\\\&amp;\\text{\u8d1f\u6570\u6839\u820d\u53bb\uff1a}m=\\dfrac{\\sqrt5-1}{2}\\Rightarrow AB=AC=\\dfrac{\\sqrt5+1}{2}\\\\&amp;\\text{\u6839\u636e\u51e0\u4f55\u5173\u7cfb\u53ca\u4e09\u89d2\u51fd\u6570\u5b9a\u4e49\uff1a}\\\\&amp;\\sin18^{\\circ}=\\dfrac{CE}{AC}=\\dfrac{\\dfrac12\\cdot BC}{AD+DC}=\\dfrac{\\dfrac12}{1+\\dfrac{\\sqrt5-1}{2}}=\\dfrac{\\sqrt5-1}{4}\\\\&amp;\\because \\sin^2\\alpha+\\cos^2\\alpha=1\\\\&amp;\\therefore \\cos18^{\\circ}=\\sqrt{1-\\sin^218^{\\circ}}=\\sqrt{\\dfrac{5+\\sqrt5}{8}}\\\\&amp;\\because S_\\triangle ABC=AC\\cdot BF=BC\\cdot AE\\Rightarrow \\dfrac{\\sqrt5+1}{2}\\cdot BF=1\\cdot AE\\\\&amp;AE=\\sqrt{(AC)^2-(\\dfrac12\\cdot BC)^2}=\\sqrt{\\Big(\\dfrac{\\sqrt5+1}{2}\\Big)^2-\\dfrac14}=\\sqrt{\\dfrac{5+2\\sqrt5}{4}}\\\\&amp;\\therefore BF=\\dfrac{\\sqrt{5+2\\sqrt5}}{\\sqrt5+1}\\\\&amp;\\therefore \\sin36^{\\circ}=\\dfrac{BF}{AB}=\\dfrac{2\\sqrt{5+2\\sqrt5}}{(\\sqrt5+1)^2}\\\\&amp;\\therefore \\cos18^{\\circ}\\sin36^{\\circ}=\\dfrac{\\sqrt{5+2\\sqrt5}\\cdot\\sqrt{5+\\sqrt5}}{\\sqrt2\\cdot(\\sqrt5+1)^2}=\\dfrac{\\sqrt{35+15\\sqrt5}}{\\sqrt2(6+2\\sqrt5)}\\\\&amp;=\\dfrac{\\sqrt5\\sqrt{7+3\\sqrt5}}{2\\sqrt2(3+\\sqrt5)}=\\dfrac{\\sqrt5\\sqrt{\\dfrac12\\cdot \\left(9+6\\sqrt{5}+5\\right)}}{2\\sqrt2(3+\\sqrt5)}=\\dfrac{\\sqrt5\\sqrt{{\\dfrac12}\\cdot\\left(3+\\sqrt5\\right)^2}}{2\\sqrt2(3+\\sqrt5)}=\\dfrac{\\sqrt5}{4}\\\\&amp;\\therefore \\bbox[yellow,5pt,border:2px solid red]{\\text{\u7528\u521d\u4e2d\u77e5\u8bc6\u6c42\u89e3\uff0c\u8ba1\u7b97\u91cf\u8fd8\u662f\u6bd4\u8f83\u5927\u7684\uff0c\u5c24\u5176\u6700\u540e\u4e00\u6b65\uff0c\u4fc4\u7f57\u65af\u7ade\u8d5b\u9898\u76ee\u633a\u751f\u731b\uff01}}\\\\&amp;\\text{\u5982\u679c\u7528\u9ad8\u4e2d\u6570\u5b66\u77e5\u8bc6\u6c42\u89e3\uff0c\u96be\u5ea6\u964d\u4f4e\u4e0d\u5c11\uff1a}\\\\&amp;\\because \\sin2\\alpha=2\\sin\\dfrac{\\alpha}{2}\\cdot\\cos\\dfrac{\\alpha}{2}\uff0c\\sin^2\\alpha+\\cos^2\\alpha=1\\\\&amp;\\therefore \\sin36^{\\circ}=2\\sin18^{\\circ}\\cos18^{\\circ}\\\\&amp;\\therefore \\cos18^{\\circ}\\sin36^{\\circ}=2\\sin18^{\\circ}\\cdot\\cos^2{18}^{\\circ}=2\\sin18^{\\circ}\\cdot(1-\\sin^2{18}^{\\circ})\\\\&amp;=2\\cdot\\dfrac{\\sqrt5-1}{4}\\cdot(1-\\dfrac{6-2\\sqrt5}{16})=\\dfrac{\\sqrt5}{4}\\\\&amp;\\bbox[yellow,6pt,border:2px solid red]{\\text{\u7528\u9ad8\u4e2d\u7684\u4e09\u89d2\u51fd\u6570\u516c\u5f0f\u6c42\u89e3\uff0c\u96be\u5ea6\u964d\u4f4e\u5f88\u591a\uff0c\u4e0d\u7528\u5316\u7b80\u590d\u6742\u6839\u5f0f\u4e86\uff01}}\\end{split}$<\/p><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-stackable-columns stk-block-columns stk-block stk-40a413a stk-block-background\" data-block-id=\"40a413a\"><style>.stk-40a413a{background-color:#ffe2c7 !important;border-top-left-radius:18px !important;border-top-right-radius:18px !important;border-bottom-right-radius:18px !important;border-bottom-left-radius:18px !important;border-style:solid !important;overflow:auto !important}.stk-40a413a:before{background-color:#ffe2c7 !important}<\/style><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-40a413a-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-ace8755\" data-v=\"4\" data-block-id=\"ace8755\"><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-ace8755-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-ace8755-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-6edba8e\" data-block-id=\"6edba8e\"><p class=\"stk-block-text__text\">\u2003\u2003<strong>\u9898\u76ee\u4e09\uff1a\u7f57\u9a6c\u5c3c\u4e9a\u5965\u6797\u5339\u514b\u521d\u4e2d\u6570\u5b66\u7ade\u8d5b\u9898\uff0c\u5df2\u77e5$a\u3001b\u3001c\\in\\mathbb Z\uff0cabc\\ne0\uff0ca\\ne c\uff0c\\dfrac a c=\\dfrac{a^2+b^2}{c^2+b^2}$\uff0c\u8bc1\u660e\uff1a$a^2+b^2+c^2\\text{\u4e0d\u662f\u8d28\u6570\u3002}$<\/strong><br>\u2003\u2003<strong>\u89e3\u9898\u601d\u8def\uff1a<\/strong>\u7c7b\u4f3c\u7684\u6570\u8bba\u65b9\u9762\u7684\u9898\u76ee\uff0c\u5012\u662f\u5728\u6570\u5b66\u7ade\u8d5b\u4e2d\u5e38\u89c1\uff0c\u9700\u8981\u6bd4\u8f83\u4e25\u8c28\u7684\u601d\u8def\uff0c\u5bf9\u8d28\u6570\u7684\u6027\u8d28\u9700\u8981\u719f\u7ec3\u638c\u63e1\uff0c\u6709\u4e00\u5b9a\u96be\u5ea6\u3002\u8fd9\u9053\u9898\u76ee\u7528\u5230\u7684\u62d3\u5c55\u4e09\u89d2\u4e0d\u7b49\u5f0f\u662f\u4e00\u4e2a\u4e0d\u5e38\u89c1\u7684\u8003\u70b9\uff0c\u5bb9\u6613\u88ab\u5ffd\u7565\u3002<br><br>$\\begin{split}\\text{\u89e3\uff1a}\\\\&amp;\\because \\dfrac a c=\\dfrac{a^2+b^2}{c^2+b^2}\\Rightarrow a(c^2+b^2)=c(a^2+b^2)\\\\&amp;\\Rightarrow ab^2-cb^2+ac^2-ca^2=0\\Rightarrow b^2(a-c)+ac(c-a)=0\\\\&amp;\\therefore (a-c)(b^2-ac)=0\\\\&amp;\\because a\\ne c\\Rightarrow a-c\\ne0\\\\&amp;\\therefore b^2-ac=0\\Rightarrow b^2=ac\\\\&amp;\\therefore a^2+b^2+c^2=a^2+2ac+c^2+b^2-2ac=(a+c)^2-b^2=(a+c+b)(a+c-b)\\\\&amp;\\therefore a\u3001b\u3001c\\in\\mathbb Z\uff0cabc\\ne0\uff0ca\\ne c\\bbox[yellow,5pt,border:2px solid red]{\\Rightarrow a^2+b^2+c^2=\\vert a+c+b\\vert\\cdot\\vert a+c-b\\vert\\gt0}\\\\&amp;\\therefore \\vert a\\vert\u3001\\vert c\\vert\\text{\u4e0d\u53ef\u80fd\u90fd\u662f$1$\uff0c\u81f3\u5c11\u6709\u4e00\u4e2a}\\geqslant2\\\\&amp;\\therefore a^2+b^2+c^2\\gt\\vert a\\vert+\\vert b\\vert+\\vert c\\vert\\\\&amp;\\bbox[yellow,5pt,border:2px solid red]{\\text{\u7531\u4e09\u89d2\u4e0d\u7b49\u5f0f\uff1a}\\vert x\\vert+\\vert y\\vert+\\vert z\\vert\\geqslant\\vert x\\pm y\\pm z\\vert}\\\\&amp;\\therefore a^2+b^2+c^2\\gt\\vert a\\vert+\\vert b\\vert+\\vert c\\vert\\geqslant\\vert a+c\\pm b\\vert\\\\&amp;\\therefore a^2+b^2+c^2\\gt\\vert a+c+b\\vert\u4e14 a^2+b^2+c^2\\gt\\vert a+c-b\\vert\\\\&amp;\\because a^2+b^2+c^2\\text{\u53ef\u4ee5\u5206\u89e3\u6210\u4e3a\u4e24\u4e2a\u5c0f\u4e8e\u5176\u672c\u8eab\u7684\u4e24\u4e2a\u6570\u7684\u4e58\u79ef} \\\\&amp;\\therefore\\text{\u6839\u636e\u8d28\u6570\u7684\u6027\u8d28\uff0c}  a^2+b^2+c^2\\text{\u4e0d\u53ef\u80fd\u662f\u8d28\u6570!}\\\\\\\\&amp;\\bbox[yellow,6pt,border:2px solid blue]{\\text{\u4ece\u8fd9\u9053\u9898\u76ee\u7684\u96be\u5ea6\u6765\u770b\uff0c\u7f57\u9a6c\u5c3c\u4e9a\u5b69\u5b50\u7684\u6570\u5b66\u6c34\u5e73\u771f\u662f\u633a\u9ad8\u7684\uff01}}\\end{split}$<\/p><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-stackable-columns stk-block-columns stk-block stk-7507b75 stk-block-background\" data-block-id=\"7507b75\"><style>.stk-7507b75{background-color:#F6F6F6 !important;border-top-left-radius:18px !important;border-top-right-radius:18px !important;border-bottom-right-radius:18px !important;border-bottom-left-radius:18px !important;border-style:solid !important;overflow:auto !important}.stk-7507b75:before{background-color:#F6F6F6 !important}<\/style><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-7507b75-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-88e39a1\" data-v=\"4\" data-block-id=\"88e39a1\"><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-88e39a1-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-88e39a1-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-67651e7\" data-block-id=\"67651e7\"><p class=\"stk-block-text__text\">\u2003\u2003<strong>\u9898\u76ee\u56db\uff1a\u6cd5\u56fd\u521d\u4e2d\u6570\u5b66\u7ade\u8d5b\u9898\uff0c\u89e3\u65b9\u7a0b\uff1a$\\sqrt{3+\\sqrt{9+x}}=\\sqrt[3]{x}$<\/strong><br>\u2003\u2003<strong>\u89e3\u9898\u601d\u8def\uff1a<\/strong>\u4e4d\u4e00\u770b\uff0c\u65b9\u7a0b\u5de6\u8fb9\u662f\u6839\u53f7\uff0c\u53f3\u8fb9\u662f\u5f00\u4e09\u6b21\u65b9\uff0c\u53bb\u6839\u53f7\u4f3c\u4e4e\u662f\u4e00\u4e2a\u4e0d\u9519\u7684\u9009\u62e9\uff0c\u4f46\u662f\u4ed4\u7ec6\u4e00\u770b\uff0c\u6bd4\u8f83\u590d\u6742\uff0c\u8ba1\u7b97\u91cf\u592a\u5927\uff0c\u4e0d\u884c\uff01\u53ea\u80fd\u4f7f\u7528\u6362\u5143\u6cd5\u53bb\u6839\u53f7\u3002<br><br>$\\begin{split}\\text{\u89e3\uff1a}\\\\&amp;\\because \\sqrt{9+x}\\geqslant0\\Rightarrow \\sqrt{3+\\sqrt{9+x}}\\geqslant\\sqrt{3}\\gt1\\\\&amp;\\therefore \\sqrt[3]{x}\\gt1\\\\&amp;\u4ee4\\sqrt[3]{x}=a(a\\gt1)\\Rightarrow x=a^3\\\\&amp;\\sqrt{3+\\sqrt{9+x}}=a\\Rightarrow 3+\\sqrt{9+x}=a^2\\Rightarrow \\sqrt{9+x}=a^2-3\\\\&amp;\\text{\u65b9\u7a0b\u4e24\u8fb9\u5e73\u65b9\u53bb\u6839\u53f7\u53ef\u5f97\uff1a}9+x=a^4+9-6a^2\\text{\u5c06$x=a^3$\u4ee3\u5165\u53ef\u5f97\uff1a}\\\\&amp;a^4-a^3-6a^2=0\\Rightarrow a^2(a^2-a-6)=0\\\\&amp;\\because a\\gt1\\Rightarrow a^2\\gt1\\\\&amp;\\therefore a^2-a-6=0\\Rightarrow (a-3)(a+2)=0\\\\&amp;\\therefore a=3(a=-2\u4e0d\u7b26\u5408\u9898\u610f\uff0c\u6545\u820d\u53bb)\\\\&amp;\\therefore x=a^3=3^3=27\\\\\\\\&amp;\\bbox[yellow,6pt,border:3px solid red]{\\boldsymbol{\\text{\u7c7b\u4f3c\u6362\u5143\u6cd5\u9700\u8981\u719f\u7ec3\u638c\u63e1\uff0c\u6cd5\u56fd\u5b69\u5b50\u7684\u6570\u5b66\u6c34\u5e73\u8ddf\u7f8e\u56fd\u5b69\u5b50\u5dee\u4e0d\u591a\uff01}}}\\end{split}$<\/p><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-stackable-columns stk-block-columns stk-block stk-3188512 stk-block-background\" data-block-id=\"3188512\"><style>.stk-3188512{background-color:#ffe2c7 !important;border-top-left-radius:18px !important;border-top-right-radius:18px !important;border-bottom-right-radius:18px !important;border-bottom-left-radius:18px !important;border-style:solid !important;overflow:auto !important}.stk-3188512:before{background-color:#ffe2c7 !important}<\/style><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-3188512-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-f0a98c4\" data-v=\"4\" data-block-id=\"f0a98c4\"><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-f0a98c4-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-f0a98c4-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-70587da\" data-block-id=\"70587da\"><p class=\"stk-block-text__text\">\u2003\u2003<strong>\u9898\u76ee\u4e94\uff1a\u6c5f\u82cf\u7701\u521d\u4e2d\u6570\u5b66\u7ade\u8d5b\u9898\uff0c\u5df2\u77e5$a\u3001b\\in\\Bbb R$\uff0c\u4e14$\\dfrac4{a^4}-\\dfrac2{a^2}=5\uff0cb^4+b^2=5$\uff0c\u6c42$\\dfrac4{a^4}+b^4$\u7684\u503c\u3002<\/strong><br>\u2003\u2003<strong>\u89e3\u9898\u601d\u8def\uff1a<\/strong>\u89c2\u5bdf\u53d1\u73b0\uff0c\u4e24\u4e2a\u6761\u4ef6\u4f3c\u4e4e\u5341\u5206\u76f8\u4f3c\uff0c\u53ef\u4ee5\u4f7f\u7528\u4e00\u79cd\u7279\u6b8a\u7684\u65b9\u5f0f\u8fdb\u884c\u6362\u5143\uff0c\u7136\u540e\u901a\u8fc7\u97e6\u8fbe\u5b9a\u7406\u8f6c\u6362\u540e\u6c42\u89e3\uff0c\u8fd9\u79cd\u601d\u8def\u5012\u662f\u5341\u5206\u5de7\u5999\u3002<br><br>$\\begin{split}\\text{\u89e3\uff1a}\\\\&amp;\\dfrac4{a^4}-\\dfrac2{a^2}=5\\Rightarrow \\left(-\\dfrac2{a^2}\\right)^2+\\left(-\\dfrac2{a^2}\\right)-5=0\\\\&amp;b^4+b^2=5\\Rightarrow \\Big(b^2\\Big)^2+b^2-5=0\\\\&amp;\\text{\u4ee4$x_1=-\\dfrac2{a^2}\uff0cx_2=b^2$}\\\\&amp;\\therefore x_{1,2}\u662f\u65b9\u7a0b\uff1ax^2+x-5=0\u7684\u4e24\u4e2a\u6839\uff01\u6839\u636e\u97e6\u8fbe\u5b9a\u7406\uff1a\\\\&amp;x_1+x_2=-1\uff0cx_1\\cdot x_2=-5\\\\&amp;\\therefore\\dfrac4{a^4}+b^4=(x_1)^2+(x_2)^2=(x_1+x_2)^2-2x_1\\cdot x_2=(-1)^2-2\\times(-5)=11\\\\\\\\&amp;\\bbox[yellow,6pt,border:2px solid red]{\\text{\u5982\u6b64\u770b\u6765\uff0c\u4e2d\u56fd\u5b69\u5b50\u7684\u6570\u5b66\u6c34\u5e73\u7684\u786e\u6bd4\u56fd\u5916\u5b69\u5b50\u7684\u6c34\u5e73\u9ad8\u591a\u4e86\u3002}} \\end{split}$<\/p><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-stackable-columns stk-block-columns stk-block stk-cc8ca7d stk-block-background\" data-block-id=\"cc8ca7d\"><style>.stk-cc8ca7d{background-color:#F6F6F6 !important;border-top-left-radius:18px !important;border-top-right-radius:18px !important;border-bottom-right-radius:18px !important;border-bottom-left-radius:18px !important;border-style:solid !important;overflow:auto !important}.stk-cc8ca7d:before{background-color:#F6F6F6 !important}<\/style><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-cc8ca7d-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-59354c5\" data-v=\"4\" data-block-id=\"59354c5\"><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-59354c5-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-59354c5-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-23f5ba2\" data-block-id=\"23f5ba2\"><p class=\"stk-block-text__text\">\u2003\u2003<strong>\u9898\u76ee\u516d\uff1a\u5317\u4eac\u5e02\u516d\u4e2d\u81ea\u4e3b\u62db\u751f\u9898\uff0c\u89e3\u65b9\u7a0b\uff1a$x^2-4x-2=\\dfrac{3}{x-3}+\\dfrac{5}{x-5}$<\/strong><br>\u2003\u2003<strong>\u89e3\u9898\u601d\u8def\uff1a<\/strong>\u5982\u679c\u76f4\u63a5\u5316\u7b80\uff0c\u51fa\u73b0\u56db\u6b21\u65b9\uff0c\u65e0\u6cd5\u6c42\u6839\u3002\u53ea\u80fd\u8bbe\u6cd5\u4f7f\u7528\u6362\u5143\u6cd5\u6c42\u89e3\u4e86\uff0c\u89c2\u5bdf\u53d1\u73b0\uff0c\u65b9\u7a0b\u7684\u5de6\u8fb9\u6709$x-4$\uff0c\u65b9\u7a0b\u7684\u53f3\u8fb9\u6709$x-3\uff0cx-5$\uff0c\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u901a\u5e38\u4f7f\u7528\u5747\u503c\u6362\u5143\u6cd5\u3002<br><br>$\\begin{split}\\text{\u89e3\uff1a}\\\\&amp;\\text{\u539f\u65b9\u7a0b\u53ef\u4ee5\u53d8\u5f62\u4e3a\uff1a}x^2-4x=\\dfrac{3}{x-3}+1+\\dfrac{5}{x-5}+1=\\dfrac{x}{x-3}+\\dfrac{x}{x-5}\\\\&amp;\\Rightarrow x\\Bigg[(x-4)-\\left(\\dfrac{1}{x-3}+\\dfrac{1}{x-5}\\right)\\Bigg]=0\\\\&amp;\\therefore x_1=0\u6216\u8005\\left(x-4\\right)-\\left(\\dfrac{1}{x-3}+\\dfrac{1}{x-5}\\right)=0\\\\&amp;\\text{\u4f7f\u7528\u5747\u503c\u6362\u5143\u6cd5\uff0c\u4ee4$t=x-4$\u5219\uff1a}\\\\&amp;t-\\Big(\\dfrac{1}{t+1}+\\dfrac{1}{t-1}\\Big)=0\\Rightarrow t-\\dfrac{2t}{t^2-1}=0\\Rightarrow t\\Big(1-\\dfrac{2}{t^2-1}\\Big)=0\\\\&amp;\\therefore t=0\\Rightarrow x-4=0\\Rightarrow x_2=4\\\\&amp;\\text{\u6216\u8005$1-\\dfrac{2}{t^2-1}=0$}\\Rightarrow t^2-1=2\\Rightarrow t^2=3\\Rightarrow t=\\pm\\sqrt{3}\\\\&amp;\\Rightarrow x-4=\\pm\\sqrt{3}\\Rightarrow x_{3,4}=4\\pm\\sqrt{3}\\\\&amp;\\therefore\\bbox[yellow,6pt,border:2px solid red]{ x_1=0\uff0cx_2=4\uff0cx_3=4+\\sqrt3\uff0cx_4=4-\\sqrt3}\\end{split}$<\/p><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u2003\u2003\u9898\u76ee\u4e00\uff1a\u4e2d\u56fd\u53f0\u6e7e\u521d\u4e2d\u6570\u5b66\u7ade\u8d5b\u9898\u76ee\uff0c\u82e5$a+b=12$\uff0c\u6c42$\\sqrt{a^2+4}+\\sqrt{b^2+4 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3,4],"tags":[],"class_list":["post-685","post","type-post","status-publish","format-standard","hentry","category-3","category-4"],"_links":{"self":[{"href":"https:\/\/itantan.eu.org\/index.php?rest_route=\/wp\/v2\/posts\/685","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/itantan.eu.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/itantan.eu.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/itantan.eu.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/itantan.eu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=685"}],"version-history":[{"count":0,"href":"https:\/\/itantan.eu.org\/index.php?rest_route=\/wp\/v2\/posts\/685\/revisions"}],"wp:attachment":[{"href":"https:\/\/itantan.eu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=685"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/itantan.eu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=685"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/itantan.eu.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=685"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}