(a+b)2≤2*(a2+b2)是什么公式？ 2(a2+b2)大于或等于(a+b)2 求解释不等式公式怎么...
\u5728\u516c\u5f0f\uff08a+b\uff092=a2+2ab+b2\u4e2d\uff0c\u5982\u679c\u6211\u4eec\u628aa+b\uff0ca2+b2\uff0cab\u5206\u522b\u770b\u505a\u4e00\u4e2a\u6574\u4f53\uff0c\u90a3\u4e48\u53ea\u8981\u77e5\u9053\u5176\u4e2d\u4e24\u9879\u7684\u503c\uff0c\u5c31\uff081\uff09\u2235a+b=6\uff0c\u2234\uff08a+b\uff092=36\uff0c\u5373a2+2ab+b2=36\uff0c\u2235ab=-27\uff0c\u2234a2+b2=36+2\u00d727=90\uff1b\uff082\uff09\u2235a+1a=5\uff0c\u2234\uff08a+1a\uff092=25\uff0c\u5373a2+2+1a2=25\uff0c\u2234a2+1a2=25-2=23\uff0e\u6545\u7b54\u6848\u4e3a\uff1a\uff081\uff0990\uff0c\uff082\uff0923\uff0e
\u7531\u5747\u503c\u4e0d\u7b49\u5f0f\uff1aa²+b²\u22652ab
2(a²+b²)\u2265a²+b²+2ab
2(a²+b²)\u2265(a+b)²
\u5c31\u662f\u8fd9\u4e48\u6765\u7684\u3002\u7531\u5747\u503c\u4e0d\u7b49\u5f0f\u7b80\u5355\u63a8\u5bfc\u5c31\u53ef\u4ee5\u5f97\u5230\u3002
a^2+b^2>=2ab 两边同时加上 a^2+b^2
所以 (a+b)2≤2*(a2+b2）
均值不等式的变形
均值不等式
2ab≤a²+b²
两边加上a²+b²
2ab+a²+b²≤a²+b²+a²+b²
(a+b)²≤2(a²+b²)
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绛旓細1銆乤2-b2=(a+b)(a-b)2銆乤2+2ab+b2=(a+b)2 3銆乤2-2ab+b2=(a-b)2 4銆乤3+b3=(a+b)(a2-ab+b2)5銆乤3-b3=(a-b)(a2+ab+b2)6銆乤3+3a2b+3ab2+b3=(a+b)3 7銆乤3-3a2b+3ab2-b3=(a-b)3 8銆乤2+b2+c2+2ab+2bc+2ca=(a+b+c)2 ...
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