Question Number 146913 by mathdanisur last updated on 16/Jul/21
$${ax}={by}={cz}=\frac{\mathrm{2}}{\mathrm{3}}\:{and}\:{ab}+{bc}+{ac}=\mathrm{36}{abc} \\ $$$${find}\:\:{x}+{y}+{z}=? \\ $$
Answered by liberty last updated on 16/Jul/21
$$\:\begin{cases}{{ax}=\frac{\mathrm{2}}{\mathrm{3}}}\\{{by}=\frac{\mathrm{2}}{\mathrm{3}}}\\{{cz}=\frac{\mathrm{2}}{\mathrm{3}}}\end{cases}\: \\ $$$$\Rightarrow{x}+{y}+{z}=\frac{\mathrm{2}}{\mathrm{3}}\left(\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}+\frac{\mathrm{1}}{{c}}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\frac{\mathrm{2}}{\mathrm{3}}\left(\frac{{ab}+{ac}+{bc}}{{abc}}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\frac{\mathrm{2}}{\mathrm{3}}\left(\frac{\mathrm{36}{abc}}{{abc}}\right)=\mathrm{24} \\ $$$$ \\ $$
Commented by mathdanisur last updated on 16/Jul/21
$${thank}\:{you}\:{Ser} \\ $$