f(x2)-f(x1)=x2^3+ax2^2-x1^3-ax1^2
=(x2-x1)(x2^2+x1x2+x1^2)+a(x2+x1)(x2-x1)
=(x2-x1)(x2^2+x1x2+x1^2+ax2+ax1)≥0
x2^2+x1x2+x1^2+ax2+ax1≥0
a≥-(x2^2+x1x2+x1^2)/(x1+x2)=-(x2+1+x1)/(1/x2+1/x1)
当x2=x1=2时,不等式右边有极小值
a≥-5
f(x2)-f(x1)=x2^3+ax2^2-x1^3-ax1^2
=(x2-x1)(x2^2+x1x2+x1^2)+a(x2+x1)(x2-x1)
=(x2-x1)(x2^2+x1x2+x1^2+ax2+ax1)≥0
x2^2+x1x2+x1^2+ax2+ax1≥0
a≥-(x2^2+x1x2+x1^2)/(x1+x2)=-(x2+1+x1)/(1/x2+1/x1)
当x2=x1=2时,不等式右边有极小值
a≥-5