Unordered triplet

Author: mathforces
Problem has been solved: 32 times

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For an unordered triplet of positive integer numbers $a$, $b$ and $c$, the following equalities hold: $$a + b + c = 25$$ $$\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{40}{99}-\frac{1}{abc}$$ Find $ab + bc + ca$.