令y=根号下2a+1+根号下2b+1则y^2=2a+1+2b+1+2根号下(2a+1)(2b+1)=4+2根号下(2a+1)(2b+1)且a+b=1,则(2a+1)+(2b+1)=4由均值不等式4>=2根号下(2a+1)(2b+1)则y^2<=4+4=8则y<=2根号2
2倍根号2
