x^2=2y+5,y^2=2x+5,求x^3+2(xy)^2+y^3我的答案是15和-37?是吗?

Question

x^2=2y+5,y^2=2x+5,求 x^3+2(xy)^2+y^3
我的答案是15和-37?是吗?

Answer 1

x^2=2y+5,
y^2=2x+5,
求 x^3+2(xy)^2+y^3
两式相减
（x+y)(x-y)=2(y-x)
x+y=-2 (1)
两式相加
x^2+y^2=2(x+y)+5=1
x^2+y^2=1 (2)
(1)平方-(2)
2xy=3
xy=1.5
x^3+2(xy)^2+y^3
=(x+y)(x^2+y^2-xy)+2(xy)^2
=.
-2*（-0.5）+2*2.25
=5.5