a²+2b²-4a+8b+20
=(a²-4a+4)+(2b²+8b+8)+8
=(a²-4a+4)+2(b²+4b+4)+8
=(a-2)²+2(b+2)²+8
因为(a-2)²≥0,2(b+2)²≥0
所以,上式≥8
当a=2,b=-2时,取最小值8