已知实数a,b满足a(a+1)-(a^+2b)=1,求a^-4ab+4b^-2a+4b的值

问题描述:

已知实数a,b满足a(a+1)-(a^+2b)=1,求a^-4ab+4b^-2a+4b的值

a(a+1)-(a²+2b)=1
a²+a-a²-2b=1
a-2b=1
a²-4ab+4b²-2a+4b
=(a²-4ab+4b²)-(2a-4b)
=(a-2b)²-2(a-2b)
=1²-2*1
=1-2
=-1