A=2x^2-3xy+y^2+x-3y,B=4x^2-6xy+2y^2+4x-y,若｜x-2a|+(y+3)^2=0,且

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/10/06 22:01:55

A=2x^2-3xy+y^2+x-3y,B=4x^2-6xy+2y^2+4x-y,若｜x-2a|+(y+3)^2=0,且B-2A=a,求A的值．
是｜x-2a|+(y+3)^2=0
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∵ |x-2a|+(y+3)²=0
∴ x=2a,y=-3
∵ A = 2x²-3xy+y²-x+2y = 8a²+16a+3
B = 4x²-6xy+2y²+3x-y = 16a²+42a+21
∴ B-2A = 16a²+42a+21-2*(8a²+16a+3)
= 10a+15
= a
∴ a = -5/3
∴ A = 8a²+16a+3 = -13/9
再问： B的化简可以详细点吗？
再答：抱歉，前面解答有误，正确如下： ∵ A = 2x²-3xy+y²+x-3y = 2*(2a)²-3*(2a)*3+3²+2a-3*3 = 2*(4a²)-18a+9+2a-9 = 8a²-16a B = 4x²-6xy+2y²+4x-y = 4*(2a)²-6*(2a)*3+2*3²+4*(2a)-3 = 4*(4a²)-36a+2*9+8a-3 = 16a²-36a+18+8a-3 = 16a²-36a+18+8a-3 = 16a²-28a+15 ∴ B-2A = 16a²-28a+15 - 2*(8a²-16a) = 16a²-28a+15-16a²+32a = 4a+15 = a ∴ a = -5 ∴ A = 8a²-16a = 8*(-5)²-16*(-5) = 200+80 = 280
再问：怪不得我算的和你不对了，这个你确定是正确的？
再答： B = 4x²-6xy+2y²+4x-y = 4*(2a)²-6*(2a)*(-3)+2*(-3)²+4*(2a)-(-3) = 4*(4a²)+36a+2*9+8a+3 = 16a²+36a+18+8a+3 = 16a²+42a+21

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