已知A=5x²y-3xy²+4xy；B=7xy²-2xy+x²y,且x+y=2,x-y=0,化简求-1/2（A+B)-A.

题目

已知A=5x²y-3xy²+4xy；B=7xy²-2xy+x²y,且x+y=2,x-y=0,化简求-1/2（A+B)-A.

答案

解
x+y=2
x-y=0
两式相加得：2x=2
∴x=y=1
-1/2(A+B)-A
=-1/2A-1/2B-A
=-3/2A-1/2B
=-3/2(5x²y-3xy²+4xy)-1/2(7xy²-2xy+x²y)
=(-15/2x²y-1/2x²y)+(9/2xy²-7/2xy²)+(-6xy+xy)
=-8x²y+xy²-5xy
=-8×1×1+1×1-5×1×1
=-8+1-5
=-12