# Why Are There So Many Powers?

Algebra Level 4

For a function $$f(x)$$ such that

$x^4\left(f(x)\right)^4+x^2=3x^3\left(f(x)\right)^2,$

let the largest possible value of $$f(2014)$$ over all possible functions $$f(x)$$ be $$M.$$ Find $$\lfloor 1000M\rfloor .$$

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