a²2+2a+b²-4b+5= (a+1)²+(b-2)²≥0
最小值0
此时a=-1,b=2
a²2+2ab+2b²-4b+5
= (a+b)²+(b-2)²+1≥1
最小值1
此时b=2,a=-2
a²2+ab+b²-4b+5
= (a+b/2)²+3/4(b²-16/3b)+5
= (a+b/2)²+3/4(b-8/3)²+5-16/3
= (a+b/2)²+3/4(b-8/3)²-1/3 ≥-1/3
最小值-1/3
此时b=8/3,a=-4/3