# Maximum Value

Algebra Level 3

If $$a, b, c$$ are non-negative real numbers subject to $$a+b+c = 4$$, then the maximum value of $$ab + bc + ca$$ is of the form $$\dfrac{x}{y}$$ (where $$x$$ and $$y$$ are coprime integers). Find $$x\times y$$.

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