化简求值:已知x、y满足:x2+y2﹣4x+6y+13=0,求代数式(3x+y)2﹣3(3x﹣y)(x+y)﹣(x﹣3y)(x+3y)的值.
题型:解答题难度:一般来源:重庆市期末题
化简求值:已知x、y满足:x2+y2﹣4x+6y+13=0,求代数式(3x+y)2﹣3(3x﹣y)(x+y)﹣(x﹣3y)(x+3y)的值. |
答案
解:原式=9x2+6xy+y2﹣3(3x2+3xy﹣xy﹣y2)﹣(x2﹣9y2) =9x2+6xy+y2﹣9x2﹣6xy+3y2﹣x2+9y2 =﹣x2+13y2 ∵x2+y2﹣4x+6y+13=0, ∴(x﹣2)2+(y+3)2=0, ∴x=2,y=﹣3, 当x=2,y=﹣3时,原式=﹣4+13×9=113. |
举一反三
计算:(﹣2ab2)3(3a2b)2+4a3b218a4b6=( ). |
计算:(1)x2﹣(x3y﹣2x2y2)﹢xy (2)(1﹣)(1+)(1+)(1+) (3)(2x﹣3y)2﹣(y+3x)(3x﹣y) (4)(2a3b2﹣4a4b3+6a5b4)÷(﹣2a3b2) |
先化简再求值:(x+y+z)2+(x﹣y﹣z)(x﹣y+z)﹣z(x+y),其中x﹣y=6,xy=21. |
解方程:3(a+5)2﹣2(3﹣a)2+(9﹣a)(9+a)=0. |
先化简再求值:(x+y+z)2+(x﹣y﹣z)(x﹣y+z)﹣z(x+y),其中x﹣y=6,xy=21. |
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