已知a,b为正整数,方程x^2+ax+2b=0与x^2+2bx+a=0都有实根,求a+b的最小值

方程有解,则有：a^2-8b>=0,4*b^2-4a>=0,
>>>>>>>> a^2>=8b,b^2>=a >>>>>>>> b^4>=8b
>>>>>>>> b^4-8b>=0 >>>>>>> b*(b^3-8)>=0
>>>>>>>> b*(b-2)*(b^2+2b+4)>=0 >>>>>>>> b*(b-2)>=0
>>>>>>>> b>=2或b>>>>>>> a(min)=4 >>>>>> (a+b)(min)=6