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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 $.





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