已知x+y=9,xy=4,则x^2+y^2=__,(x-y)^2=_

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x+y=9对它两边平方就得（x+y)2=92即x2+y2+2xy=81又有xy=4代进去就是x2+y2+2×4=81从而解得x2+y2=81-8=73,(x-y)^2=x2+y2-2xy=73-2×4=73-8=65于是x^2+y^2=73
,(x-y)^2=65...

千问 | 2013-3-16 16:35:58 | 显示全部楼层

x+y=9平方一下x^2+2xy+y^2=81x^2+y^2=81-2xy=81-8=73 (x-y)^2=x^2-2xy+y^2=73-2*4=65...

千问 | 2013-3-16 16:35:58 | 显示全部楼层

（x+y）2=81x2+y2+2xy=81x2+y2=81-2xy=73（x-y）2=（x+y）2-4xy=81-16=65...

千问 | 2013-3-16 16:35:58 | 显示全部楼层

x2+y2=(x+y)2-2xy=92-2×4=81-8=73(x-y)2=(x+y)2-4xy=92-4×4=81-16=65...

千问 | 2013-3-16 16:35:58 | 显示全部楼层

X^2+Y^2=(X+Y)^2-2xy=9^2-2*4=18-8=10(x-y)^2=X^2+y^2-2XY=10-8=2...

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