不等式与不等式组
证明下列各式:
(1) a的平方+b的平方大于等于2ab
(2) m分之24+6m大于等于24(m>0)
人气:183 ℃ 时间:2020-02-05 21:47:38
解答
a2+b2-2ab=(a-b)2
因为(a-b)2≥0,即a2+b2-2ab≥0
所以a2+b2≥2ab
24/m+6m-24
=(24+6m2-24m)/m
=6(4+m2-4m)/m
=6(m-2) 2/m
因为m >0
所以6(m-2) 2/m≥0,即24/m+6m-24≥0
所以24/m+6m≥24
注:紧挨在字母后面的2代表平方
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