# Switching numerator and denominator

Algebra Level 2

$\dfrac{5}{a} = b+c, \quad \dfrac{10}{b} = c+a, \quad \dfrac{13}{c} = a+b.$

Let $$a$$, $$b$$, $$c$$ be positive real numbers satisfying the equations above.

Compute the product of $$a, b,$$ and $$c.$$

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