{"id":1945,"date":"2021-11-03T16:08:41","date_gmt":"2021-11-03T07:08:41","guid":{"rendered":"https:\/\/www.roundown.net\/nyushi\/?p=1945"},"modified":"2021-11-14T08:08:30","modified_gmt":"2021-11-13T23:08:30","slug":"htb201601","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/htb201601\/","title":{"rendered":"\u4e00\u6a4b\u59272016\uff1a\u7b2c1\u554f"},"content":{"rendered":"<hr \/>\n<p>\\(6 \\cdot 3^{3x} +1 = 7 \\cdot 5^{2x}\\) \u3092\u6e80\u305f\u3059 \\(0\\) \u4ee5\u4e0a\u306e\u6574\u6570 \\(x\\) \u3092\u3059\u3079\u3066\u6c42\u3081\u3088.<\/p>\r\n<hr \/>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<ul>\r\n<li><p>\\(x = 0\\) \u306e\u3068\u304d\r\n\\[\r\n6 \\cdot 1 +1 = 7 = 7 \\cdot 1\r\n\\]<\/li>\r\n<li><p>\\(x = 1\\) \u306e\u3068\u304d\r\n\\[\r\n6 \\cdot 27 +1 = 163 \\neq 175 = 7 \\cdot 25\r\n\\]<\/li>\r\n<li><p>\\(x = 2\\) \u306e\u3068\u304d\r\n\\[\r\n6 \\cdot 729 +1 = 4375 = 7 \\cdot 625\r\n\\]<\/li>\r\n<\/ul>\r\n<p>\u4ee5\u4e0b\u3067\u306f, \\(x \\geqq 3\\) \u304c\u89e3\u3067\u306a\u3044\u3053\u3068\u3092\u793a\u3059.<br \/>\r\n\\(x \\geqq 2\\) \u306e\u3068\u304d\u306b \\(6 \\cdot 3^{3x} +1 \\geqq 7 \\cdot 5^{2x}\\) ... [1] \u304c\u6210\u7acb\u3059\u308b\u3068\u4eee\u5b9a\u3059\u308b\u3068\r\n\\[\\begin{align}\r\n6 \\cdot 27^{x+1} +1 & \\geqq ( 25 +2 ) ( 7 \\cdot 25^x -1 ) +1 \\quad ( \\ \\text{\u2235} \\ [1] \\ )\\\\\r\n& = 7 \\cdot 25^{x+1} +14 \\cdot 25^x -26 \\\\\r\n& \\gt 7 \\cdot 25^{x+1}\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \u5e30\u7d0d\u7684\u306b \\(n \\geqq 3\\) \u306b\u304a\u3044\u3066\u306f\r\n\\[\r\n6 \\cdot 3^{3x} +1 \\gt 7 \\cdot 5^{2x}\r\n\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u89e3\u306f\r\n\\[\r\nx = \\underline{0 , 2}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(6 \\cdot 3^{3x} +1 = 7 \\cdot 5^{2x}\\) \u3092\u6e80\u305f\u3059 \\(0\\) \u4ee5\u4e0a\u306e\u6574\u6570 \\(x\\) \u3092\u3059\u3079\u3066\u6c42\u3081\u3088.","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[161],"tags":[146,162],"class_list":["post-1945","post","type-post","status-publish","format-standard","hentry","category-hitotsubashi_2016","tag-hitotsubashi","tag-162"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1945","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/comments?post=1945"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1945\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1945"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1945"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1945"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}