Question

已知x(x-1)-(x^2-y)=6,则(x^2+y^2)/2-xy=多少？

Answer 1

x(x-1)-(x^2-y)=6,
-x+y=6
y-x=6
所以
(x^2+y^2)/2-xy
=1/2 (x-y)²
=1/2 ×6²
=1/2×36
=18

Answer 2

解：x(x-1)-(x^2-y)=6可化为：
x^2-x-x^2+y=6
y-x=6
(x^2+y^2)/2-xy可化为：
（y^2-2xy+x^2+2xy）/2-xy
（y-x）^2/2+xy-xy
y-x=6
（y-x）^2/2+xy-xy=6^2/2=18
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