a²+2b²-4a+8b+20
=a²-4a+4+2b²+8b+16
=(a-2)²+2(b²+4b+4)+8
=(a-2)²+2(b+2)²+8
很明显 当(a-2)²=0,2(b+2)²=0时取最小值
即a=2,b=-2时最小值为8