{"id":8443,"date":"2023-01-16T10:16:00","date_gmt":"2023-01-16T02:16:00","guid":{"rendered":"https:\/\/blog.iyatt.com\/?p=8443"},"modified":"2024-05-08T15:10:04","modified_gmt":"2024-05-08T07:10:04","slug":"%e5%9b%9b%e4%b8%aa%e5%9d%87%e5%80%bc%e4%b8%8d%e7%ad%89%e5%bc%8f","status":"publish","type":"post","link":"https:\/\/blog.iyatt.com\/?p=8443","title":{"rendered":"\u4e0d\u7b49\u5f0f"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 ez-toc-wrap-center counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title ez-toc-toggle\" style=\"cursor:pointer\">\u76ee\u5f55<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/blog.iyatt.com\/?p=8443\/#%E5%9D%87%E5%80%BC%E4%B8%8D%E7%AD%89%E5%BC%8F\" >\u5747\u503c\u4e0d\u7b49\u5f0f<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/blog.iyatt.com\/?p=8443\/#%E5%85%B3%E7%B3%BB\" >\u5173\u7cfb<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/blog.iyatt.com\/?p=8443\/#%E8%AF%81%E6%98%8E\" >\u8bc1\u660e<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/blog.iyatt.com\/?p=8443\/#%E5%87%A0%E4%BD%95\" >\u51e0\u4f55<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/blog.iyatt.com\/?p=8443\/#%E6%95%B0%E5%AD%A6\" >\u6570\u5b66<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/blog.iyatt.com\/?p=8443\/#%E7%BB%9D%E5%AF%B9%E5%80%BC%E4%B8%89%E8%A7%92%E4%B8%8D%E7%AD%89%E5%BC%8F\" >\u7edd\u5bf9\u503c\u4e09\u89d2\u4e0d\u7b49\u5f0f<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/blog.iyatt.com\/?p=8443\/#%E6%9F%AF%E8%A5%BF%E4%B8%8D%E7%AD%89%E5%BC%8F\" >\u67ef\u897f\u4e0d\u7b49\u5f0f<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"%E5%9D%87%E5%80%BC%E4%B8%8D%E7%AD%89%E5%BC%8F\"><\/span>\u5747\u503c\u4e0d\u7b49\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8c03\u548c\u5e73\u5747\u6570 <code class=\"katex-inline\">\\frac{2}{\\frac{1}{a}+\\frac{1}{b}}<\/code><br \/>\n\u51e0\u4f55\u5e73\u5747\u6570 <code class=\"katex-inline\">\\sqrt{ab}<\/code><br \/>\n\u7b97\u6570\u5e73\u5747\u6570 <code class=\"katex-inline\">\\frac{a+b}{2}<\/code><br \/>\n\u5e73\u65b9\u5e73\u5747\u6570 <code class=\"katex-inline\">\\sqrt{\\frac{a^2+b^2}{2}}<\/code><\/p>\n<h3><span class=\"ez-toc-section\" id=\"%E5%85%B3%E7%B3%BB\"><\/span>\u5173\u7cfb<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><code class=\"katex-inline\">\\frac{2}{\\frac{1}{a}+\\frac{1}{b}}\\le\\sqrt{ab}\\le\\frac{a+b}{2}\\le\\sqrt{\\frac{a^2+b^2}{2}}<\/code>\uff0ca=b\u65f6\uff0c\u7b49\u53f7\u6210\u7acb<\/p>\n<h3><span class=\"ez-toc-section\" id=\"%E8%AF%81%E6%98%8E\"><\/span>\u8bc1\u660e<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h4><span class=\"ez-toc-section\" id=\"%E5%87%A0%E4%BD%95\"><\/span>\u51e0\u4f55<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><img decoding=\"async\" data-src=\"https:\/\/blog.iyatt.com\/wp-content\/uploads\/2023\/01\/image-1673834236045.png\" alt=\"file\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" class=\"lazyload\" style=\"--smush-placeholder-width: 912px; --smush-placeholder-aspect-ratio: 912\/497;\" \/><\/p>\n<p>\u5176\u4e2d <code class=\"katex-inline\">BO\\bot AD\uff0cCE\\bot AD\uff0cEF\\bot CO<\/code><\/p>\n<p>\u8bbe AE = a\uff0cDE = b<br \/>\n\u7b97\u6570\u5747\u503c <code class=\"katex-inline\">AO=DO=BO=CO=\\frac{a+b}{2}<\/code>\uff08\u534a\u5f84\uff09<br \/>\n\u51e0\u4f55\u5747\u503c <code class=\"katex-inline\">CE=\\sqrt{AE\\cdot DE}=\\sqrt{ab}<\/code>(\u5c04\u5f71\u5b9a\u7406)<br \/>\n\u5e73\u65b9\u5747\u503c <code class=\"katex-inline\">BE=\\sqrt{BO^2+EO^2}=\\sqrt{\\frac{a+b}{2}^2+(a-\\frac{a+b}{2})^2}=\\sqrt{\\frac{a^2+b^2}{2}}<\/code><br \/>\n\u8c03\u548c\u5747\u503c <code class=\"katex-inline\">CF=\\frac{CE^2}{CO}=\\frac{ab}{\\frac{a+b}{2}}=\\frac{1}{\\frac{1}{a}+\\frac{1}{b}}<\/code>(\u5c04\u5f71\u5b9a\u7406)<\/p>\n<p><code class=\"katex-inline\">BE\\ge AO\\ge CE\\ge CF<\/code><\/p>\n<p>\u6ce8\uff1a<br \/>\n\u5c04\u5f71\u5b9a\u7406<\/p>\n<p><img decoding=\"async\" data-src=\"https:\/\/blog.iyatt.com\/wp-content\/uploads\/2023\/01\/image-1673835654743.png\" alt=\"file\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" class=\"lazyload\" style=\"--smush-placeholder-width: 942px; --smush-placeholder-aspect-ratio: 942\/472;\" \/><\/p>\n<p>\u5176\u4e2d <code class=\"katex-inline\">AC\\bot BC\uff0cCD\\bot AB<\/code>\uff0c\u6709<br \/>\n<code class=\"katex-inline\">CD^2=AD\\cdot BD<\/code><br \/>\n<code class=\"katex-inline\">AC^2=AB\\cdot AD<\/code><br \/>\n<code class=\"katex-inline\">BC^2=AB\\cdot BD<\/code><br \/>\n<code class=\"katex-inline\">AC\\cdot BC=AB\\cdot CD<\/code><\/p>\n<h4><span class=\"ez-toc-section\" id=\"%E6%95%B0%E5%AD%A6\"><\/span>\u6570\u5b66<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<pre><code class=\"language-katex\">(a-b)^2\\ge0 \\\\\na^2+b^2\\ge2ab \\\\\n\\frac{a^2+b^2}{4}\\ge\\frac{2ab}{4} \\\\\n\\frac{2a^2+2b^2}{4}\\ge\\frac{a^2+b^2+2ab}{4}=\\frac{(a+b)^2}{4} \\\\\n\\sqrt{\\frac{a^2+b^2}{2}}\\ge\\frac{a+b}{2} \\\\\n\\ \\\\\n(a-b)^2\\ge0 \\\\\na^2+b^2\\ge2ab \\\\\na^2+b^2+2ab\\ge4ab \\\\\n\\frac{(a+b)^2}{4}\\ge ab \\\\\n\\frac{a+b}{2}\\ge\\sqrt{ab} \\\\\n\\ \\\\\n(a-b)^2\\ge0 \\\\\na^2+b^2\\ge2ab \\\\\na^2+b^2+2ab\\ge4ab \\\\\nab(a^2+b^2+2ab)\\ge4(ab)^2 \\\\\nab\\ge\\frac{4}{\\frac{(a+b)^2}{(ab)^2}} \\\\\n\\sqrt{ab}\\ge\\frac{2}{\\frac{a+b}{ab}}=\\frac{2}{\\frac{1}{a}+\\frac{1}{b}}<\/code><\/pre>\n<h2><span class=\"ez-toc-section\" id=\"%E7%BB%9D%E5%AF%B9%E5%80%BC%E4%B8%89%E8%A7%92%E4%B8%8D%E7%AD%89%E5%BC%8F\"><\/span>\u7edd\u5bf9\u503c\u4e09\u89d2\u4e0d\u7b49\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><code class=\"katex-inline\">||a|-|b||\\le|a\\pm b|\\le|a|+|b|<\/code><\/p>\n<p><code class=\"katex-inline\">ab\\le0\u65f6\uff0c||a|-|b||\\le|a+b|\u548c|a-b|\\le|a|+|b|\u7b49\u53f7\u6210\u7acb<\/code><br \/>\n<code class=\"katex-inline\">ab\\ge0\u65f6\uff0c||a|-|b||\\le|a-b|\u548c|a+b|\\le|a|+|b|\u7b49\u53f7\u6210\u7acb<\/code><\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E6%9F%AF%E8%A5%BF%E4%B8%8D%E7%AD%89%E5%BC%8F\"><\/span>\u67ef\u897f\u4e0d\u7b49\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><code class=\"katex-inline\">(a_1b_1+a_2b_2+...+a_nb_n)^2\\le(a_1^2+a_2^2+...+a_n^2)(b_1^2+b_2^2+...+b_n^2)<\/code>\uff0c<code class=\"katex-inline\">\\frac{a_1}{b_1}=\\frac{a_2}{b_2}=\\cdots=\\frac{a_n}{b_n}\u65f6\uff0c\u7b49\u53f7\u6210\u7acb<\/code><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5747\u503c\u4e0d\u7b49\u5f0f \u8c03\u548c\u5e73\u5747\u6570 \\frac{2}{\\frac{1}{a}+\\frac{1}{b}} \u51e0\u4f55\u5e73\u5747\u6570 \\sq [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"zakra_page_container_layout":"customizer","zakra_page_sidebar_layout":"customizer","zakra_remove_content_margin":false,"zakra_sidebar":"customizer","zakra_transparent_header":"customizer","zakra_logo":0,"zakra_main_header_style":"default","zakra_menu_item_color":"","zakra_menu_item_hover_color":"","zakra_menu_item_active_color":"","zakra_menu_active_style":"","zakra_page_header":true,"_lmt_disableupdate":"no","_lmt_disable":"no","footnotes":""},"categories":[1,612],"tags":[],"class_list":["post-8443","post","type-post","status-publish","format-standard","hentry","category-all","category-612"],"modified_by":"IYATT-yx","_links":{"self":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts\/8443","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=8443"}],"version-history":[{"count":0,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts\/8443\/revisions"}],"wp:attachment":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8443"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8443"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8443"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}