已知:x+y=15,x^2+y^2=113,求代数式x^2-xy+y^2的值

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已知:x+y=15,x^2+y^2=113,求代数式x^2-xy+y^2的值
已知:x+y=15,x^2+y^2=113,求代数式x^2-xy+y^2的值

已知:x+y=15,x^2+y^2=113,求代数式x^2-xy+y^2的值
x+y=15 -> (x+y)^2=x^2+2xy+y^2=225 -> 113+2xy=225 -> xy=56
x^2+y^2-xy=113-56=56

2xy=(x+y)²-(x²+y²)=225-113=112;
xy=56;
x^2-xy+y^2=113-56=57;

俊狼猎英团队为您解答

(X+Y)^2=225
X^2+Y^2+2XY=225
XY=56

x^2-xy+y^2
=(X+Y)^2-3XY
=15^2-3×56
=57

∵x+y=15,x^2+y^2=113
∴(x+y)²=x²+y²+2xy
即225=113+2xy
xy=6
x^2-xy+y^2
=113-6
=107

x+y=15,x^2+y^2=113
xy=1/2*[(x+y)^2-x^2-y^2]=1/2*(225-113)=57
x^2-xy+y^2
=x^2+y^2-xy
=113-57
=56

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