# Maximize The Difference!

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For all continuous functions $$f:[0,1]\rightarrow \mathbb{R}$$, let

$K_f=\int_0^1 x^2 f(x) ~\text{d}x$

$L_f=\int_0^1 x (f(x))^2~\text{d}x$

The maximum value of $$K_f-L_f$$ over all such functions can be represented as $$\dfrac a b$$. Find $$a+b$$.

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