Question Number 173115 by dragan91 last updated on 06/Jul/22
$$\mathrm{a}+\mathrm{b}=\mathrm{b}+\mathrm{c}=\mathrm{a}+\mathrm{c}=\mathrm{abc} \\ $$$$\left(\mathrm{a},\mathrm{b},\mathrm{c}\right)=? \\ $$
Commented by kaivan.ahmadi last updated on 06/Jul/22
$${a}+{b}={b}+{c}\Rightarrow{a}={c} \\ $$$${a}+{b}={a}+{c}\Rightarrow{b}={c} \\ $$$$\Rightarrow{a}={b}={c}={x} \\ $$$$\mathrm{2}{x}={x}^{\mathrm{3}} \Rightarrow{x}^{\mathrm{3}} −\mathrm{2}{x}=\mathrm{0}\Rightarrow{x}\left({x}^{\mathrm{2}} −\mathrm{2}\right)=\mathrm{0}\Rightarrow \\ $$$$ \\ $$$$\left\{_{{x}^{\mathrm{2}} =\mathrm{2}\Rightarrow{x}=\pm\sqrt{\mathrm{2}}} ^{{x}=\mathrm{0}} \right. \\ $$$$ \\ $$