A=a²+4ab+5b²+b+100
=(a²+4ab+4b²)+(b²+b+1/4)+(100-1/4)
=(a+2b)²+(b+1/2)²+399/4.
∴a=-2b且b=-1/2,即a=1,b=-1/2时,
所求最小值为:399/4.