a+b>=2根号下ab
ab<=1/4
1/2(a+b)+1/4+ab<=1
(a+1/2)(b+1/2)<=1
2*根号下【(a+1/2)(b+1/2)】<=2
a+b+1+2*根号下【(a+1/2)(b+1/2)】<=4
[根号下(a+1/2)+根号下（b+1/2)]^2<=4
根号下(a+1/2)+根号下（b+1/2)<=2

(根号(a+1/2)+根号(b+1/2))²<=2(a+1/2+b+1/2)=2×(1+1)=4
开方得
根号(a+1/2)+根号(b+1/2)<=2
基本不等式：(x+y)²<=2(x²+y²)
证明很简单,略