已知x^2+y^2=7,xy=-2.求5X^2-3(XY-Y^2)-11XY-2(-X^2-2Y^2)的值thank

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已知x^2+y^2=7,xy=-2.求5X^2-3(XY-Y^2)-11XY-2(-X^2-2Y^2)的值thank
已知x^2+y^2=7,xy=-2.求5X^2-3(XY-Y^2)-11XY-2(-X^2-2Y^2)的值
thank

已知x^2+y^2=7,xy=-2.求5X^2-3(XY-Y^2)-11XY-2(-X^2-2Y^2)的值thank
5x²-3(xy-y²)-11xy-2(-x²-2y²)
=5x²-3xy+3y²-11xy+2x²+4y²
=7x²+7y²-14xy
=7(x²+y²)-14xy
=7×7-14×(-2)
=49+28
=77

解
x²+y²=7
xy=-2


5x²-3(xy-y²)-11xy-2(-x²-2y²)
=5x²-3xy+3y²-11xy+2x²+4y²
=(5x²+2x²)+(-3xy-11xy)+(3y²+4y²)
=7x²+7y²-14xy
=7(x²+y²)-14xy
=7×7-14×(-2)
=49+28
=77

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