已知x2-4x+2y2-4y+6=0,先化简再求值:(2x+y)(2x-y)-(2x-y)2.

问题描述:

已知x2-4x+2y2-4y+6=0,先化简再求值:(2x+y)(2x-y)-(2x-y)2

x2-4x+2y2-4y+6=x2-4x+2y2-4y+2+4=(x-2)2+2(y-1)2=0,∴x-2=0,y-1=0,解得x=2,y=1,∵(2x+y)(2x-y)-(2x-y)2,=4x2-y2-(4x2-4xy+y2),=4x2-y2-4x2+4xy-y2,=-2y2+4xy,=-2+8=6....