Question

不等式证明求解已知:正数x1,x2,x3……xn 满足x1+x2+x3+……+xn=1

Answer 1

显然n>=2
1/(x(1-x^3))=1/x+x^2/(1-x^3)
而1/x1+1/x2+1/x3+...+1/xn>=n*(1/(1/n))=n^2
xi^2/(1-xi^3)>0
所以原式>1/x1+1/x2+1/x3+...+1/xn>=n^2>=4
命题得证