inequality.......................

a_i>0;i=1,2,3,4.........n
(n-1)s=a₁+a₂+a₃+a₄+..............a_n
prove that
a₁.a_₂a₃..........a_n>= (n-1)ⁿ(s-a₁).(s-a₂).(s-a₃)(s-a₄).........(s-a_n)

1 Answers

(n-1)s -a₂ -a₃ -a₄.....a_n=a₁

a₁=(s-a₂) +(s-a₃) +(s-a₄)...........(s-a_n)

>(n-1) [(s-a₂)(s-a₃)....(s-a_n)]^1/(n-1) ........since AM > GM

similarly write other inequalities for a₂ a₃ a ₄ and so on and then multiply u will get teh req inequality

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