已知x+y=12,xy=9,且x＜y,求(x^1/2-y^1/2)/(x^1/2+y^1/2)的值
问题描述：
已知x+y=12,xy=9,且x＜y,求(x^1/2-y^1/2)/(x^1/2+y^1/2)的值
答
x＜y推出(x^1/2-y^1/2)/(x^1/2+y^1/2)＜0
思路就是平方开根号
所以：(x^1/2-y^1/2)/(x^1/2+y^1/2)
=-{[(x^1/2-y^1/2)]^2/[(x^1/2+y^1/2)]^2}^1/2
=-{[x+y-2(xy)^1/2]/[x+y+2(xy)^1/2}^1/2
=-[(12-6)/(12+6)]^1/2
=-(1/3)^1/2