> 数学 >
已知a>0,b>0,a+b=1,求证:(a+1/a)(b+1/b)≥25/4
人气:402 ℃ 时间:2020-06-08 18:57:43
解答
左式=ab+a/b+1/ab+b/a
=(a2b2+a2+1+b2)/ab
=[a2b2+(1-2ab)+1]/ab
=[(ab-1)2+1]/ab
(ab-1)2+1≥25/16,0
推荐
猜你喜欢
© 2024 79432.Com All Rights Reserved.
电脑版|手机版