# 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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