Question Number 151070 by mathdanisur last updated on 18/Aug/21
$$\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{30}\:\:\:\mathrm{and}\:\:\:\mathrm{a};\mathrm{b};\mathrm{c}>\mathrm{0} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\frac{\mathrm{1}}{\mathrm{a}}\:+\:\frac{\mathrm{1}}{\mathrm{b}}\:+\:\frac{\mathrm{1}}{\mathrm{c}} \\ $$
Commented by john_santu last updated on 18/Aug/21
$$\frac{\mathrm{1}}{\mathrm{a}}+\frac{\mathrm{1}}{\mathrm{b}}+\frac{\mathrm{1}}{\mathrm{c}}\geqslant\frac{\left(\mathrm{1}+\mathrm{1}+\mathrm{1}\right)^{\mathrm{2}} }{\mathrm{a}+\mathrm{b}+\mathrm{c}}=\frac{\mathrm{9}}{\mathrm{30}}=\frac{\mathrm{3}}{\mathrm{10}} \\ $$
Commented by mathdanisur last updated on 18/Aug/21
$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{Ser} \\ $$$$\mathrm{what}\:\mathrm{an}\:\mathrm{inequality}\:\mathrm{it}\:\mathrm{was}\:\mathrm{please} \\ $$
Commented by Ari last updated on 20/Aug/21
$$\mathrm{Can}\:\mathrm{you}\:\mathrm{explain}\:\mathrm{please}\:\mathrm{how}\:\mathrm{thid}\:\mathrm{inequality}\:\mathrm{is}? \\ $$
Commented by Ari last updated on 20/Aug/21
$$\mathrm{Could}\:\mathrm{you}\:\mathrm{explain}\:\mathrm{please}\:\mathrm{how}\:\mathrm{this}\:\mathrm{enequality}\:\mathrm{is}? \\ $$