Question Number 55889 by behi83417@gmail.com last updated on 05/Mar/19
$$\:\:\:\:\:\boldsymbol{\mathrm{a}}=\boldsymbol{\mathrm{b}}^{\mathrm{2}} +\boldsymbol{\mathrm{bc}}+\boldsymbol{\mathrm{c}}^{\mathrm{2}} \\ $$$$\:\:\:\:\:\boldsymbol{\mathrm{b}}=\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\boldsymbol{\mathrm{ac}}+\boldsymbol{\mathrm{c}}^{\mathrm{2}} \\ $$$$\:\:\:\:\:\boldsymbol{\mathrm{c}}=\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\boldsymbol{\mathrm{ab}}+\boldsymbol{\mathrm{b}}^{\mathrm{2}} \\ $$$$\:\:\:\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\::\:\:\boldsymbol{\mathrm{a}},\:\:\boldsymbol{\mathrm{b}},\:\:\boldsymbol{\mathrm{c}}. \\ $$
Answered by MJS last updated on 05/Mar/19
$${a}={b}={c}=\mathrm{0}\:\vee\:{a}={b}={c}=\frac{\mathrm{1}}{\mathrm{3}} \\ $$