2 Equations, 5 Variables

Algebra Level 4

\(x_1, x_2, x_3, x_4\) and \(x_5\) are reals such that \(x_1+x_2+x_3+x_4+x_5=8\) and \(x_1^2+x_2^2+x_3^2+x_4^2+x_5^2=16.\) What is the largest possible value of \(x_5?\)

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