# Infinity is lovely

Algebra Level 5

$K= \large \sqrt{5 + \sqrt{5-\sqrt{5+\sqrt{5-\sqrt{5+\ldots}}}}}$

If $$K$$ can be expressed in simplest form as $$\dfrac{a+\sqrt{b}}{c}$$, where $$a,b,c$$ are positive integers, find the value of $$a^2+b^2+c^2$$.

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