Question

若x^2+xy-2y^2=0,则(x^2+3xy+y^2)/(x^2+y^2)=______?

若x^2+xy-2y^2=0,则(x^2+3xy+y^2)/(x^2+y^2)=______?

Answer 1

分解x^2+xy-2y^2=0,(x+2y)(x-y)=0,x=-2y或
x=y
(x^2+3xy+y^2)/(x^2+y^2)
=「(x^2+xy-2y^2)+(2xy+3y^2)」/(x^2+y^2)
=(2xy+3y^2)/(x^2+y^2)
将x=-2y
，x=y分别代入
可得
原式=-1/5或5/2
妈妈呀
输这个可真麻烦!