Question

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*

Answer 1

(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