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2017 InIMC keystage3-IWYMIC individual Question 9

xIMC · 2017 InIMC keystage3-IWYMIC individual

Question 9

The sum of the non-negative real numbers $x_1,x_2,\ldots,x_8$ is 8. Find the largest possible value of the expression $x_1x_2+x_2x_3+x_3x_4+\cdots+x_7x_8$.