a,b是正实数且a+b=1 证明：ab+1/ab〉=4+1/4
问题描述：
a,b是正实数且a+b=1 证明：ab+1/ab〉=4+1/4
答
a+b>=2√ab
√ababab+1/ab>=1/4+4
所以成立
答
ab+1/ab＝ab+(a+b)/ab=ab+1/a+1/b
=ab+(a+b)/a+(a+b)b
=ab+2+a/b+b/a
>=ab+2+2
=ab+4
=a*(1-a)+4
那么设y＝－a^2+a+4 (0