若﹙2x+y-1﹚²+|x-2y-3|=0,求代数式﹙2x+y﹚﹙2x-y﹚-﹙x+2y﹚﹙x-2y-1)的值

问题描述:

若﹙2x+y-1﹚²+|x-2y-3|=0,求代数式﹙2x+y﹚﹙2x-y﹚-﹙x+2y﹚﹙x-2y-1)的值

﹙2x+y-1﹚²+|x-2y-3|=0
∴﹛2x+y-1=0
x-2y-3=0
∴2x+y=1
x-2y=3
解得x=1,y=-1
∴﹙2x+y﹚﹙2x-y﹚-﹙x+2y﹚﹙x-2y-1)
=2x-y-(x+2y)×(3-1)
=2x-y-2x-4y
=-5y
=5