- 证明题设a.b>0,且a+b=1,求证:(a+1/a)(b
- 设a.b>0,且a+b=1,求证:(a+1/a)(b+1/b)大于等于25/4。
- 0
=1/4+4=17/4函数在(0,1)上是减函数
a/b+b/a>=2
(a+1/a)(b+1/b)>=25/4
方法二
左式=ab+a/b+1/ab+b/a
=(a2b2+a2+1+b2)/ab
=[a2b2+(1-2ab)+1]/ab
=[(ab-1)2+1]/ab
a+b=1
ab<=(a+b/2)^2=1/4
所以:(ab-1)^2+1≥25/16,0