HMMT 2005 F2

Find three real numbers $a<b<c$ satisfying:

$\begin{aligned} a+b+c & =21 / 4 \\ 1 / a+1 / b+1 / c & =21 / 4 \\ a b c & =1 \end{aligned}$

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{1}{4}, 1, 4

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