# Minimal value

Algebra Level 5

Given an integer $$\displaystyle n \ge 2$$ .The minimal value of $\displaystyle \frac{x_{1}^{5}}{x_{2}+{x_{3}}+…+x_{n}} + \frac{x_{2}^{5}}{x_{1}+x_{3}+…+x_{n}} +…+ \frac{x_{n}^{5}}{x_{1}+…x_{n-1}}$ ,for positive real numbers $$x_{1},x_{2},…,x_{n}$$ subject to the condition that sum of their squares is 1 , can be expressed as $$\displaystyle \frac{\alpha}{n(n-\beta)}$$ where $$\displaystyle \alpha$$ and $$\displaystyle \beta$$ are positive integers then what is the value of $$\displaystyle \alpha+\beta$$

×