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

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

若x^2+xy-2y^2=0,则(x^2+3xy+y^2)/(x^2+y^2)=多少
x^2+xy-2y^2=0
(x+2y)(x-y)=0
x=-2y or x=y
x=-2y
(x^2+3xy+y^2)/(x^2+y^2)
=(4y^2-6y^2+y^2)/5y^2
=-1/5
x=y
(x^2+3xy+y^2)/(x^2+y^2)
=5y^2/2y^2
=5/2

(x+2y)(x-y)=0
x=-2y或x=y
所以原式=(4y²-6y²+y²)/(4y²+y²)=-1/5
或原式=(y²+3y²+y²)/(y²+y²)=5/2