若x+y=m,xy=n,则x2+y2=______,(x-y)2=______,x2-xy+y2=______.
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若x+y=m,xy=n,则x2+y2=______,(x-y)2=______,x2-xy+y2=______.
![若x+y=m,xy=n,则x2+y2=______,(x-y)2=______,x2-xy+y2=______.](/uploads/image/z/19047125-29-5.jpg?t=%E8%8B%A5x%2By%3Dm%EF%BC%8Cxy%3Dn%EF%BC%8C%E5%88%99x2%2By2%3D______%EF%BC%8C%EF%BC%88x-y%EF%BC%892%3D______%EF%BC%8Cx2-xy%2By2%3D______%EF%BC%8E)
∵x+y=m,
∴(x+y)2=m2,即x2+y2+2xy=m2,
∴x2+y2=m2-2xy=m2-2n;
(x-y)2=x2+y2-2xy=m2-2n-2n=m2-4n;
x2-xy+y2=x2+y2-xy=m2-2n-n=m2-3n.
∴(x+y)2=m2,即x2+y2+2xy=m2,
∴x2+y2=m2-2xy=m2-2n;
(x-y)2=x2+y2-2xy=m2-2n-2n=m2-4n;
x2-xy+y2=x2+y2-xy=m2-2n-n=m2-3n.
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