8/3 women day=83 followers-problem 34.

Algebra Level 5

x 1 3 + x 2 3 + ⋯ + x 83 3 x_{1}^{3}+x_{2}^{3}+\cdots+x_{83}^{3}

Given that x 1 ; x 2 ; … ; x 83 x_{1};x_{2};\ldots ;x_{83} are positive real integers and their product is 83 83 .Find the maximum value of the expression above.

Special problem
Set .


The answer is 571869.

Son Nguyen by Son Nguyen , 20, Vietnam

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1 solution

Nicola M.
Mar 8, 2016

83 is a prime number so only pruced by 1x83. So here we have 82 times 1 to the power of 3 plus 83 to the power of 3. 1^3 remains 1, so:

82x(1)+83^3=571.869

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