Question Number 213607 by tri26112004 last updated on 10/Nov/24
$${Give}\:{a},{b},{c}\:>\:\mathrm{0}\:{such}\:{that} \\ $$$${ab}+{bc}+{ca}={abc} \\ $$$${Prove}\:{that}\:: \\ $$$${a}+{b}+{c}\geqslant\mathrm{4}\left(\frac{{a}}{{bc}}+\frac{{b}}{{ca}}+\frac{{c}}{{ab}}\right)+\mathrm{5} \\ $$