x^2-xy=2,y^2-xy=8,x^2-y^2

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x^2-xy=2,y^2-xy=8,x^2-y^2
x^2-xy=2,y^2-xy=8,x^2-y^2

x^2-xy=2,y^2-xy=8,x^2-y^2
x^2-xy=2 ①
y^2-xy=8 ②
①-②得到
x^2-y^2=-6

x^2-xy=2
x(x-y)=2 ①
y^2-xy=8
y(y-x)=8
y(x-y)=-8②
①+②的(x-y)(x+y)=-6
即x^2-y^2=-6

x^2-xy=2 得：x^2=2+xy
y^2-xy=8得：y^2=8+xy
x^2-y^2=（2+xy）-（8+xy）=-6

因x^2-xy=2 y^2-xy=8
列式为x^2-xy-（y^2-xy）
=x^2-xy-y^2+xy
-xy与xy可抵消
则x^2-y^2=2-8
=-6
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