已知x^2-4x+2y^2-4y+6=0,先简化,再求值：（2x+y）(2x-y)-(2x-y)^2

来源：学生作业学帮网编辑：学帮网时间：2024/05/14 16:33:14

即(x²-4x+4)+2(y²-2y+1)=0
(x-2)²+2(y-1)²=0
所以x-2=y-1=0
x=2,y=1
原式=4x²-y²-4x²+4xy-y²
=4xy-2y²
=8-2
=6

x^2-4x+2y^2-4y+6=0
（x-4x+4)+2(y²-2y+1)=0
(x-2)²+2(y-1)²=0
x-2=0,y-1=0
x=2, y=1
：（2x+y）(2x-y)-(2x-y)^2
=(4+1)(4-1)-(4-1)²
=15-9
=6

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