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What is the largest positive integer n such that a^2 b 29 + c 31 + b^2 c 29 + a 31 + c^2 a 29 + b 31 n(a+b+c) holds for all positive real numbers a,b,c.

Correct answer

14

Step-by-step solution

Since a^2 x + b^2 y + c^2 z (a+b+c)^2 x+y+z So, a^2 b 39 + c 31 + b^2 c 29 + a 31 + c^2 a 29 + b 31 (a+b+c)^2 a ( 1 29 + 1 31 )+b ( 1 29 + 1 31 )+c ( 1 29 + 1 31 ) (a+b+c) ( 1 29 + 1 31 ) a+b+c 60 29 31 29 31 60 (a+b+c) 14.98(a+b+c) So, n =14

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