{"id":1416,"date":"2026-01-13T23:56:00","date_gmt":"2026-01-13T15:56:00","guid":{"rendered":"https:\/\/mondayqueen.top\/?p=1416"},"modified":"2026-03-03T07:54:10","modified_gmt":"2026-03-02T23:54:10","slug":"%e6%95%99%e9%ab%98%e4%b8%ad%e8%a1%a8%e4%be%84%e5%a5%b3%e5%81%9a%e4%b8%8d%e7%ad%89%e5%bc%8f%e9%a2%98%e7%9a%8410%e7%a7%8d%e6%96%b9%e6%b3%95","status":"publish","type":"post","link":"https:\/\/mondayqueen.top\/index.php\/2026\/01\/13\/%e6%95%99%e9%ab%98%e4%b8%ad%e8%a1%a8%e4%be%84%e5%a5%b3%e5%81%9a%e4%b8%8d%e7%ad%89%e5%bc%8f%e9%a2%98%e7%9a%8410%e7%a7%8d%e6%96%b9%e6%b3%95\/","title":{"rendered":"\u6559\u9ad8\u4e2d\u8868\u4f84\u5973\u505a\u4e0d\u7b49\u5f0f\u9898\u768410\u79cd\u65b9\u6cd5"},"content":{"rendered":"\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u201c\u4f60\u5148\u7406\u89e3\u8fd95\u79cd\u65b9\u6cd5\uff0c\u6211\u8fd8\u67095\u79cd\u65b9\u6cd5\u201d<\/p>\n<\/blockquote>\n\n\n\n<p>\u8fd9\u4e2a\u9898\u957f\u8fd9\u6837\uff1a<\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mtext>\u82e5<\/mtext><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><msup><mi>y<\/mi><mn>2<\/mn><\/msup><mo>=<\/mo><mn>1<\/mn><mtext>\uff0c<\/mtext><mtext>\u5219<\/mtext><mn>3<\/mn><mi>x<\/mi><mo>+<\/mo><mn>4<\/mn><mi>y<\/mi><mtext>\u7684<\/mtext><mtext>\u6700<\/mtext><mtext>\u5927<\/mtext><mtext>\u503c<\/mtext><mtext>\u662f<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">\u82e5x^2+y^2 = 1\uff0c\u52193x+4y\u7684\u6700\u5927\u503c\u662f<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">1. \u5224\u522b\u5f0f<\/h3>\n\n\n\n<p>\u4ee43x+4y = k\uff0c\u5219y = (k-3x)\/4\uff0cx<sup>2<\/sup>+y<sup>2<\/sup> = 1\u53ef\u5199\u6210x<sup>2<\/sup>+((k-3x)\/4)<sup>2<\/sup>=1\uff0c\u65b9\u7a0b\u6709\u89e3\uff0c\u5224\u65ad\u5224\u522b\u5f0f\u0394<strong>\u2265<\/strong>0<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2. \u6570\u5f62\u7ed3\u5408<\/h3>\n\n\n\n<p>\u76f4\u7ebf3x+4y = z\uff0c\u5373y=-3x\/4 + z\/4\u4e0e\u5355\u4f4d\u5706\u76f8\u5207\u65f6\u622a\u8ddd\u7edd\u5bf9\u503c\u6700\u5927\uff0c\u5f53\u7136\u6211\u4eec\u53d6\u4e0e\u5706\u7b2c\u4e00\u8c61\u9650\u90e8\u5206\u76f8\u5207\u7684\u89e3<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3. \u4e09\u89d2\u6362\u5143<\/h3>\n\n\n\n<p>\u4ee4x = cos\u03b8\uff0cy = sin\u03b8\uff0c\u52193x+4y = 3cos\u03b8+4sin\u03b8 = 5sin(\u03b8+\u03c6)\uff08\u7528\u4e86\u8f85\u52a9\u89d2\u516c\u5f0f\uff0c\u4e0d\u9700\u8981\u77e5\u9053\u03c6\u5177\u4f53\u662f\u591a\u5c11\uff0c\u4e0d\u8fc7\u8fd9\u4e2a\u89d2\u633a\u7279\u6b8a\uff0c\u5e94\u8be5\u662f53\u5ea6\uff09<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">4. \u5411\u91cf<\/h3>\n\n\n\n<p>\u4ee4<strong>a<\/strong> = (3,4)\uff0c<strong>b<\/strong> = (x,y)\uff0c|<strong>b<\/strong>| = 1\uff0c<strong>a<\/strong>\u00b7<strong>b\u2264<\/strong>|<strong>a<\/strong>||<strong>b<\/strong>|<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">5. \u67ef\u897f\u4e0d\u7b49\u5f0f<\/h3>\n\n\n\n<p>(x<sup>2<\/sup>+y<sup>2<\/sup>)(3<sup>2<\/sup>+4<sup>2<\/sup>)<strong>\u2265<\/strong>(3x+4y)<sup>2<\/sup><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">6. \u6743\u65b9\u548c\u4e0d\u7b49\u5f0f<\/h3>\n\n\n\n<p>\u5176\u5b9e\u8ddf\u67ef\u897f\u662f\u7b49\u4ef7\u7684\u7f62\uff0c\u53ea\u662f\u6743\u65b9\u548c\u662f\u6211\u9ad8\u4e2d\u671f\u95f4\u7279\u522b\u559c\u6b22\u7528\u7684\uff0c\u59dc\u59d0\u7684\u6069\u60c5\u8fd8\u4e0d\u5b8c<\/p>\n\n\n\n<p>x<sup>2<\/sup>+y<sup>2<\/sup> = (3x)<sup>2<\/sup>\/9+(4y)<sup>2<\/sup>\/16<strong>\u2265<\/strong>(3x+4y)<sup>2<\/sup>\/(3<sup>2<\/sup>+4<sup>2<\/sup>)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">7. \u5bf9\u5076\u5f0f<\/h3>\n\n\n\n<p>(3x+4y)<sup>2<\/sup>+(4x-3y)<sup>2<\/sup> = 25<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">8. \u9f50\u6b21\u5316<\/h3>\n\n\n\n<p>\u4ee4t = y\/x\uff0c3x+4y = <math data-latex=\"\\sqrt{\\frac{(3x+4y)^2}{x^2+y^2}}\"><semantics><msqrt><mfrac><mrow><mo form=\"prefix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">(<\/mo><mn>3<\/mn><mi>x<\/mi><mo>+<\/mo><mn>4<\/mn><mi>y<\/mi><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><\/mrow><mrow><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><msup><mi>y<\/mi><mn>2<\/mn><\/msup><\/mrow><\/mfrac><\/msqrt><annotation encoding=\"application\/x-tex\">\\sqrt{\\frac{(3x+4y)^2}{x^2+y^2}}<\/annotation><\/semantics><\/math> = <math data-latex=\"\\sqrt{\\frac{16t^2+24t+9}{t^2+1}}\"><semantics><msqrt><mfrac><mrow><mn>16<\/mn><msup><mi>t<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mn>24<\/mn><mi>t<\/mi><mo>+<\/mo><mn>9<\/mn><\/mrow><mrow><msup><mi>t<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mn>1<\/mn><\/mrow><\/mfrac><\/msqrt><annotation encoding=\"application\/x-tex\">\\sqrt{\\frac{16t^2+24t+9}{t^2+1}}<\/annotation><\/semantics><\/math>\uff0c\u8fd9\u91cc\u6709\u7b97\u8fd9\u4e2a\u51fd\u6570\u7684\u6700\u5927\u503c<\/p>\n\n\n\n<p>\u4ee4z = <math data-latex=\"\\frac{16t^2+24t+9}{t^2+1}\"><semantics><mfrac><mrow><mn>16<\/mn><msup><mi>t<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mn>24<\/mn><mi>t<\/mi><mo>+<\/mo><mn>9<\/mn><\/mrow><mrow><msup><mi>t<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mn>1<\/mn><\/mrow><\/mfrac><annotation encoding=\"application\/x-tex\">\\frac{16t^2+24t+9}{t^2+1}<\/annotation><\/semantics><\/math>\uff0c\u6574\u7406\u4e3a\u5173\u4e8ez\u7684\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\uff1a(z\u221216)t<sup>2<\/sup>\u221224t+(z\u22129)=0\uff0c\u5224\u522b\u5f0f \u0394\u22650<\/p>\n\n\n\n<ol class=\"wp-block-list\"><\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">9. \u6c42\u5bfc<\/h3>\n\n\n\n<p>\u662f\u6211\u6700\u559c\u6b22\u7684\u6c42\u5bfc\u73af\u8282<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">10. \u62c9\u683c\u6717\u65e5\u6570\u4e58<\/h3>\n\n\n\n<p>\u5927\u5b66\u5b66\u7684\u3002\u4ee4f(x,y,\u03bb) = 3x+4y+\u03bb(x<sup>2<\/sup>+y<sup>2<\/sup>-1)\uff0c\u5206\u522b\u6c42f\u5bf9x\uff0c\u5bf9y\uff0c\u5bf9\u03bb\u7684\u504f\u5bfc\uff0c\u4ee4\u5176\u4e3a0\uff0c\u7b97\u51fax=3\/5\uff0cy=4\/5<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u201c\u4f60\u5148\u7406\u89e3\u8fd95\u79cd\u65b9\u6cd5\uff0c\u6211\u8fd8\u67095\u79cd\u65b9\u6cd5\u201d \u8fd9\u4e2a\u9898\u957f\u8fd9\u6837\uff1a 1. \u5224\u522b\u5f0f \u4ee43x+4y = k\uff0c\u5219y = [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"rank_math_lock_modified_date":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1416","post","type-post","status-publish","format-standard","hentry","category-im-a-nb-programmer"],"_links":{"self":[{"href":"https:\/\/mondayqueen.top\/index.php\/wp-json\/wp\/v2\/posts\/1416","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mondayqueen.top\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mondayqueen.top\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mondayqueen.top\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mondayqueen.top\/index.php\/wp-json\/wp\/v2\/comments?post=1416"}],"version-history":[{"count":1,"href":"https:\/\/mondayqueen.top\/index.php\/wp-json\/wp\/v2\/posts\/1416\/revisions"}],"predecessor-version":[{"id":1417,"href":"https:\/\/mondayqueen.top\/index.php\/wp-json\/wp\/v2\/posts\/1416\/revisions\/1417"}],"wp:attachment":[{"href":"https:\/\/mondayqueen.top\/index.php\/wp-json\/wp\/v2\/media?parent=1416"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mondayqueen.top\/index.php\/wp-json\/wp\/v2\/categories?post=1416"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mondayqueen.top\/index.php\/wp-json\/wp\/v2\/tags?post=1416"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}