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Algebra Level 5

Let S=(k=14xkxk+1)2S=\left(\sum_{k=1}^{4}x_kx_{k+1}\right)^2

Find the maximum of SS when k=15xk2=2\sum_{k=1}^{5}x_k^2=2 where x1,...,x5x_1,...,x_5 are positive real numbers.

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