[a根號(hào)下(x+y)]^2-[根號(hào)下x+根號(hào)下y]^2=
(a^2-1)x+(a^2-1)y-2根號(hào)下(xy)>=0
=>(a^2-1)(根號(hào)下x-根號(hào)下y)^2+[(a^2-1)*2-2]根號(hào)下(xy)>=0
=>a^2-1>=0,[(a^2-1)*2-2]>=0
=>a^2>=2
a必須大于0,否則不等式不成立,所以a>=根號(hào)2.實(shí)數(shù)a最小值為根號(hào)2.