求方程x+y=x^2-xy+y^2+1的实数解

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求方程x+y=x^2-xy+y^2+1的实数解求方程x+y=x^2-xy+y^2+1的实数解求方程x+y=x^2-xy+y^2+1的实数解x+y=x^2-xy+y^2+1则有;y^2+(-x-1)y+

求方程x+y=x^2-xy+y^2+1的实数解
求方程x+y=x^2-xy+y^2+1的实数解

求方程x+y=x^2-xy+y^2+1的实数解
x+y=x^2-xy+y^2+1
则有;
y^2+(-x-1)y+x^2-x+1=0
判别式是;
(-x-1)^2-4(x^2-x+1)
=x^2+2x+1-4x^2+4x-4
=-3x^2+6x-3
=-3(x^2-2x+1)
=-3(x-1)^2

1/2(x-y)^2+1/2(x-1)^2+1/2(y-1)^2=0
x=y=1