若3x²-4xy+y²=﹣3,2x²+3xy-2y²=8,求5x²-18xy+7y²的值
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/29 17:30:46
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若3x²-4xy+y²=﹣3,2x²+3xy-2y²=8,求5x²-18xy+7y²的值
若3x²-4xy+y²=﹣3,2x²+3xy-2y²=8,求5x²-18xy+7y²的值
若3x²-4xy+y²=﹣3,2x²+3xy-2y²=8,求5x²-18xy+7y²的值
设5x²-18xy+7y²=m(3x²-4xy+y²)+n(2x²+3xy-2y²)
=(3m+2n)x²-(4m-3n)xy+(m-2n)y²
则:3m+2n=5,4m-3n=18,m-2n=7 同时成立,得到m=3,n=-2
因此:5x²-18xy+7y²=3×(-3)+(-2)×8=-9-16=-25
∵3x²-4xy+y²=﹣3 ,2x²+3xy-2y²=8
∴9x²-12xy+3y²=﹣9,4x²+6xy-4y²=16
两式相减:(9x²-12xy+3y²)-(4x²+6xy-4y²)=-9-16
化简后得:5x²-118xy+7y²=﹣25