# $$\sqrt{4} = 2$$

Algebra Level 4

Consider the function $$f: \mathbb{R} \to \mathbb{R}$$ such that, for two defined constants $$a,b$$, $f(x) = \dfrac{a^x - b^x}{a-b}.$

We know that $$f(0) = 0, \; f(1) = 1, \; f(2) = \sqrt{2}, \; f(3) = \sqrt{3}$$.

If $$f(4) = w_1\sqrt{w_2-\sqrt{w_3}}$$, where $$w_1, w_2, w_3$$ are all integers with $$w_3$$ is square-free, find $$w_1 + w_2 + w_3$$.

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