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Let x1,x2,…,xnx_1, x_2, \dots, x_nx1,x2,…,xn be positive reals satisfying x1x2⋯xn=1x_1x_2 \cdots x_n = 1x1x2⋯xn=1.
Find the maximum value of 1n−1+x1+1n−1+x2+⋯+1n−1+xn. \dfrac{1}{n-1+x_1} + \dfrac{1}{n-1+x_2} + \dots + \dfrac{1}{n-1+x_n} . n−1+x11+n−1+x21+⋯+n−1+xn1.
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