已知a不等于0,比较(a平方+根号2*a+1)(a平方-根号2*a+1)与(a平方+a+1)(a平方-a+1)的大小.
人气:129 ℃ 时间:2020-03-27 22:17:47
解答
(a^2+√2a+1)(a^2-√2a+1)=(a^2+1)^2-2a^2 ①
(a^2+a+1)(a^2-a+1)=(a^2+1)^2-a^2 ②
②-①=a^2>0
所以②>①
所以(a^2+a+1)(a^2-a+1)>(a^2+√2a+1)(a^2-√2a+1)
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