Minimal value

Algebra Level 5

Given an integer n2\displaystyle n \ge 2 .The minimal value of x15x2+x3++xn+x25x1+x3++xn++xn5x1+xn1 \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 x1,x2,,xn x_{1},x_{2},…,x_{n} subject to the condition that sum of their squares is 1 , can be expressed as αn(nβ)\displaystyle \frac{\alpha}{n(n-\beta)} where α\displaystyle \alpha and β\displaystyle \beta are positive integers then what is the value of α+β\displaystyle \alpha+\beta

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