已知x+y=1,xy=-二分之一,求x（x+y)(x-y)-x(x+y)²
问题描述：
已知x+y=1,xy=-二分之一,求x（x+y)(x-y)-x(x+y)²
答
由已知，有
x+y=1，xy=-1/2，x²-x=1/2
于是
x（x+y)(x-y)-x(x+y)²
=x·1·(x-y)-x·1²
=x²-xy-x
=x²-（-1/2）-x
=x²-x+1/2
=1/2+1/2
=1
或者先化简：
x（x+y)(x-y)-x(x+y)²
=x(x+y)[(x-y)-(x+y)]
=x(x+y)(x-y-x-y)
=-2xy(x+y)
=-2×(-1/2)×1
=1
答
X(X^2-Y^2)-X(X^2+Y^2+2XY)=x^3-xy^2-x^3+xY^2-2xy=2xy=-1
答
x（x+y)(x-y)-x(x+y)²
=x(x+y)[(x-y)-(x+y)]
=x(x+y)(x-y-x-y)
=-2xy(x+y)
=-2×(-1/2)×1
=1