|x+y+1|+(2x-y-2)^2=0,求(2x-y)^2-2(2x-y)(2x+y)+(2x+y)^2

来源：百度知道编辑：UC知道时间：2024/06/05 04:41:41

步骤详细写

因|x+y+1|大于等于0，(2x-y-2)^2也是大于等于0
所以要使|x+y+1|+(2x-y-2)^2=0成立，只能是|x+y+1|=0且(2x-y-2)^2=0
由|x+y+1|=0得x+y=-1
由(2x-y-2)^2=0得2x-y=2
联立解得x=1/3 y=-4/3

(2x-y)^2-2(2x-y)(2x+y)+(2x+y)^2是完全平方式a^2-2ab+b^2=(a-b)^2
所以(2x-y)^2-2(2x-y)(2x+y)+(2x+y)^2
=[（2x-y）-（2x+y）]^2
=(-2y)^2
=4y^2
=4(-4/3)^2
=64/9

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