Question Number 126165 by TheMexicanTacosG last updated on 17/Dec/20
$${if}:\:\:\:{b}^{\mathrm{2}} \:=\:−\mathrm{3}\:−{c}^{\mathrm{2}} \:+\mathrm{2}\left({a}−{b}−{c}\right)\:−{a}^{\mathrm{2}} \\ $$$$ \\ $$$${calculate}:\:{a}\:+\:{b}\:+\:{c}\:=\:? \\ $$
Commented by PRITHWISH SEN 2 last updated on 18/Dec/20
$$\left(\mathrm{a}^{\mathrm{2}} \:−\mathrm{2a}+\mathrm{1}\right)+\left(\mathrm{b}^{\mathrm{2}} +\mathrm{2b}+\mathrm{1}\right)+\left(\mathrm{c}^{\mathrm{2}} +\mathrm{2c}+\mathrm{1}\right)=\mathrm{0}\: \\ $$$$\left(\mathrm{a}−\mathrm{1}\right)^{\mathrm{2}} +\left(\mathrm{b}+\mathrm{1}\right)^{\mathrm{2}} +\left(\mathrm{c}+\mathrm{1}\right)^{\mathrm{2}} =\:\mathrm{0} \\ $$$$\Rightarrow\:\boldsymbol{\mathrm{a}}=\:\mathrm{1},\:\boldsymbol{\mathrm{b}}=−\mathrm{1},\:\boldsymbol{\mathrm{c}}=−\mathrm{1} \\ $$$$\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{b}}+\boldsymbol{\mathrm{c}}=\mathrm{1}−\mathrm{1}−\mathrm{1}=−\mathrm{1} \\ $$