已知x+y=6,xy=4,x>y,则√x-√y／√x+√y=?

题目

已知x+y=6,xy=4,x>y,则√x-√y／√x+√y=?

答案

(√x-√y)/(√x+√y)
=(√x-√y)²/(x-y)
=(x+y-2√xy)/(x-y)
√xy=2
x-y=√(x+y)²-4xy=√20=2√5
(√x-√y)/(√x+√y)
=2/2√5
=√5/5