Question Number 40321 by faaiz last updated on 19/Jul/18
$$\mathrm{If}\:{abc}=\mathrm{8}\:\mathrm{and}\:\frac{\mathrm{1}}{{a}}\:+\:\frac{\mathrm{1}}{{b}}\:+\:\frac{\mathrm{1}}{{c}}\:=\:\frac{\mathrm{3}}{\mathrm{2}}\:\mathrm{then} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:{ab}+{bc}+{ca}. \\ $$
Commented by math khazana by abdo last updated on 19/Jul/18
$$\Rightarrow{abc}\left(\frac{\mathrm{1}}{{a}}+\:\frac{\mathrm{1}}{{b}}\:+\frac{\mathrm{1}}{{c}}\right)=\frac{\mathrm{3}}{\mathrm{2}}{abc}\Rightarrow \\ $$$${bc}\:+{ac}\:+{ab}\:=\frac{\mathrm{3}}{\mathrm{2}}.\mathrm{8}\:\Rightarrow{ab}\:+{bc}\:+{ca}=\mathrm{12}\:. \\ $$