Question Number 213726 by hardmath last updated on 14/Nov/24
$$\mathrm{ax}\:=\:\mathrm{by}\:=\:\mathrm{cz}\:=\:\mathrm{36} \\ $$$$\frac{\mathrm{1}}{\mathrm{x}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{y}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{z}}\:\:=\:\:\frac{\mathrm{1}}{\mathrm{9}} \\ $$$$\mathrm{a}\:+\:\mathrm{b}\:+\:\mathrm{c}\:=\:? \\ $$
Answered by Rasheed.Sindhi last updated on 14/Nov/24
$${a}=\frac{\mathrm{36}}{{x}},\:{b}=\frac{\mathrm{36}}{{y}},\:{c}=\frac{\mathrm{36}}{{z}} \\ $$$${a}+{b}+{c}=\frac{\mathrm{36}}{{x}}+\frac{\mathrm{36}}{{y}}+\frac{\mathrm{36}}{{z}}=\mathrm{36}\left(\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{y}}+\frac{\mathrm{1}}{{z}}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{36}\left(\frac{\mathrm{1}}{\mathrm{9}}\right)=\mathrm{4} \\ $$