(3×+y)²-(x-3y)²
x²+y²-4x+6y+13=0,求(3x+y)²-3(3x+y)(x+y)-(x-3y)(x+3y)值....
x²+y²-4x+6y+13=0,求(3x+y)²-3(3x+y)(x+y)-(x-3y)(x+3y)值.
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∵x²+y²-4x+6y+13=0,
∴﹙x²-4x+4﹚+﹙y²+6y+9﹚=0
﹙x-2﹚²+﹙y+3﹚²=0
解得:x=2,y=﹣3
化简,得
原式=(3x+y)[(3x+y﹚-3﹙x+y﹚]-﹙x²-9y²﹚
=﹙3x+y﹚﹙﹣2y﹚-x²+9y²
=﹣6xy-2y²-x²+9y²
=﹣6xy+7y²-x²
把x=2,y=﹣3代入上式,得
=﹣6×2×﹙﹣3﹚+7×﹙﹣3﹚²-2²
=36+63-4
=95
∴﹙x²-4x+4﹚+﹙y²+6y+9﹚=0
﹙x-2﹚²+﹙y+3﹚²=0
解得:x=2,y=﹣3
化简,得
原式=(3x+y)[(3x+y﹚-3﹙x+y﹚]-﹙x²-9y²﹚
=﹙3x+y﹚﹙﹣2y﹚-x²+9y²
=﹣6xy-2y²-x²+9y²
=﹣6xy+7y²-x²
把x=2,y=﹣3代入上式,得
=﹣6×2×﹙﹣3﹚+7×﹙﹣3﹚²-2²
=36+63-4
=95
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