已知非零实数x,y满足:x2+xy-2y2=0,求(x2+3y+y2)/(x2+y2)的值

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由x2+xy-2y2=0,
x2-y2+xy-y2=0,
(x+y)(x-y)+(x-y)y=0,
(x-y)(x+2y)=0.
得x-y=0或者x+2y=0.
1)当x-y=0,x=y.
(x2+3y+y2)/(x2+y2)=(x2+3x+x2)/(x2+x2)=(2x2+3x)/(2x2)=1+3/2x;
2)当x+2y=0,x=-2y.
(x2+3y+y2)/(x2+y2)=(4y2+3y+y2)/(4y2+y2)=(5y2+3y)/(5y2)=1+3/5y.
再问：值是多少？？？？
再答：一个方程,有二个求知数,不能求出值! 只能简化,算不出值!
再问：对不起，题目错啦，不是(x2+3y+y2)/(x2+y2)，正确的是：（x2+3xy+y2）/（x2+y2），前面是对的
再答：那后面变为 1)当x-y=0,x=y. (x2+3xy+y2)/(x2+y2)=(x2+3x^2+x2)/(x2+x2)=(5x2)/(2x2)=5/2; 2)当x+2y=0,x=-2y. (x2+3xy+y2)/(x2+y2)=(4y2-6y2+y2)/(4y2+y2)=(-y2)/(5y2)=-1/5. 这样就正确了!

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