a,b是正实数且a+b=1 证明：ab+1/ab〉=4+1/4

题目

a,b是正实数且a+b=1 证明：ab+1/ab〉=4+1/4

答案

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