x²+y²-4x+6y+13=0,求(3x+y)²-3(3x+y)(x+y)-(x-3y)(x+3y)值.
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/18 05:36:05
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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.
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,
∴﹙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
这是一个非负数之和等于0的题目。题中算式x²+y²-4x+6y+13=0可以整理为
(x-2)^2+(y+3)^2=0;
要使这个式子结果为0 ,必须(x-2)^2=0且(y+3)^2=0;得出
x=2,y=-3.后面就好算了。我不细算了。
x²+y²-4x+6y+13=0
(x-2)²+(y+3)²=0
x=2,y=-3
(3x+y)²-3(3x-y)(x+y)-(x-3y)(x+3y)
=(6-3)²-3(6+3)(2-3)-(2+9)(2-9)
=9+27+77
=113