# Recurring Styles #5 - Really a unique Solution?

Algebra Level 5

$\large{f_{n+1}(x) = \sqrt{x^2 + 6f_n(x)}, \quad f_0(x) = 8}$

Define a sequence of functions $$f_0 , f_1, f_2 , \ldots$$ such that it satisfies the above conditions, for whole numbers $$n$$, and real $$x$$. For every positive integer $$n$$, solve the equation $${f_n(x) = 2x}$$, for $${x}$$.

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