Question

已知x(2x-y)=y(y-2x)(xy≠0),求(x的平方+y的平方)/xy的值

Answer 1

x(2x-y)=y(y-2x)(xy≠0),

2x²-xy=y²-2xy

2x²+xy-y²=0

(2x-y)(x+y)=0

2x-y=0,x+y=0

y=2x或y=-x

若y=2x,(x²+y²)/xy=(x²+4x²)/2x²=5/2

若y=x,(x²+y²)/xy=(x²+x²)/(-x²)=-5