# Reverse Engineer This Transcendental Equation!

Algebra Level 5

Let $$a$$ be any natural number, and let $$f(x)={ a }^{ 2 }{ x }^{ 2 }-x-{ 1 }$$. Consider

$${ f(x) }^{ { f(x) }^{ f(x) } }= { 2015 }$$.

If the sum of all solutions for $$x$$ is $$k$$, determine $$\frac { { \pi }^{ 2 } }{ k }$$. (This means if for some value of $$x$$ you can set a value of $$a$$ such that it satisfies the equation, then that value of $$x$$ is a solution)

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