Question Number 214454 by hardmath last updated on 09/Dec/24
$$\mathrm{a},\mathrm{b},\mathrm{c}\:\in\:\mathbb{R}^{+} \\ $$$$\mathrm{S}\:\:=\:\:\frac{\mathrm{9a}}{\mathrm{b}\:+\:\mathrm{c}}\:\:+\:\:\frac{\mathrm{16b}}{\mathrm{a}\:+\:\mathrm{c}}\:\:+\:\:\frac{\mathrm{49c}}{\mathrm{a}\:+\:\mathrm{b}} \\ $$$$\boldsymbol{\mathrm{min}}\left(\mathrm{S}\right)\:=\:? \\ $$
Commented by Ghisom last updated on 09/Dec/24
$${S}>\mathrm{24} \\ $$$$\mathrm{min}\:\left({S}\right)\:\mathrm{does}\:\mathrm{not}\:\mathrm{exist}\:\mathrm{for}\:{a},\:{b},\:{c}\:>\mathrm{0} \\ $$