a +b =4
b=4-a
a^2+b^2
=a^2+(4-a)^2
=a^2+16-8a+a^2
=2a^2-8a+16
=2(a^2-4a)+16
=2(a^2-4a+4)+16-8
=2(a-2)^2+8
因为a>=0,则当a=2时取得最小值8