已知非零实数x,y满足：x^2+xy-2y^2=0,求(x^2+3xy+y^2)/(x^2+y^2)
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x^2+xy-2y^2=0
==> (x +2y)(x - y) = 0
==> x = -2y, or x = y
(1) x = - 2y
(x^2+3xy+y^2)/(x^2+y^2)
= (4y^2 - 6y^2 + y^2) / (5y^2)
= -y^2 / (5y^2)
= - 1/5
(2) x = y
(x^2+3xy+y^2)/(x^2+y^2)
= (y^2 + 3y^2 + y^2) / (y^2 +y^2)
= 5y^2 /2y^2
= 5/2
==> (x +2y)(x - y) = 0
==> x = -2y, or x = y
(1) x = - 2y
(x^2+3xy+y^2)/(x^2+y^2)
= (4y^2 - 6y^2 + y^2) / (5y^2)
= -y^2 / (5y^2)
= - 1/5
(2) x = y
(x^2+3xy+y^2)/(x^2+y^2)
= (y^2 + 3y^2 + y^2) / (y^2 +y^2)
= 5y^2 /2y^2
= 5/2
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