已知x和y满足2(x-y)-(x-3y)=1/2,求4^x*2^y*2^y-2^2x+1*4^y

题目

已知x和y满足2(x-y)-(x-3y)=1/2,求4^x*2^y*2^y-2^2x+1*4^y

答案

已知：2(x-y)-(x-3y)=1/2,那么：
2x-2y-x+3y=1/2
即得：x+y=1/2
所以：
4^x*2^y*2^y-2^2x+1*4^y
=2^(2x)*2^(2y) - 2*2^(2x)*2^(2y)
=2^(2x+2y) - 2*2^(2x+2y)
=-2^[2(x+y)]
=-2^[2*(1/2)]
= -2^1
= -2