已知(x-2)2+|xy-4|=0,求3x2y+{-2x2y-[-2xy+(x2y-4x2)-xy]+xy2}.

问题描述:

已知(x-2)2+|xy-4|=0,求3x2y+{-2x2y-[-2xy+(x2y-4x2)-xy]+xy2}.

3x2y+{-2x2y-[-2xy+(x2y-4x2)-xy]+xy2}
=3x2y+{-2x2y-[-2xy+x2y-4x2-xy]+xy2}
=3x2y+{-2x2y+2xy-x2y+4x2+xy+xy2}
=3x2y-2x2y+2xy-x2y+4x2+xy+xy2
=3xy+xy2+4x2
∵(x-2)2+|xy-4|=0,
∴x-2=0,xy-4=0,
∴x=2,y=2,
把x=2,y=2代入原式得:
=3×2×2+2×22+4×22
=36.