若(x*x+y*y)(x*x+y*y)-4x*x*y*y=0,求代数式(x*x+5xy+y*y)/(x*x+2xy+y*

(x*x+y*y)(x*x+y*y)-4x*x*y*y
=(x^4-2x^2y^2+y^4)
=(x^2-y^2)^2
=0
x^2=y^2
x/y=±1
(x*x+5xy+y*y)/(x*x+2xy+y*y)
=[(x/y)^2+5x/y+1] / [(x/y)^2+2x/y+1)
=(1±5+1)/(1±2+1)
=(2±5)/(2±2)
因为分母不可能为2-2=0
所以,原式=(2+5)/(2+2)=7/4