已知x＞0,y＞0,n＞1且x－√xy－2y=0求(2x－√xy)／(y＋2√xy)

题目

已知x＞0,y＞0,n＞1且x－√xy－2y=0求(2x－√xy)／(y＋2√xy)

答案

x－√xy－2y=0 x＞0,y＞0
x=a^2,y=b^2,a2-ab-2b2=(a+b)(a-2b)=0 ,得到a=2b,x=4y
(2x－√xy)／(y＋2√xy)
=(2x－x+2y)／(y＋2x-4y)
=(x+2y)(2x-3y)
=6y*5y
=30y^2