Question Number 150889 by mathdanisur last updated on 16/Aug/21
Answered by dumitrel last updated on 16/Aug/21
$$\Leftrightarrow{a}^{\mathrm{2}} +{a}\left({b}+{c}+{d}\right)+\left({b}+{c}+{d}\right)^{\mathrm{2}} \geqslant\mathrm{0}\Leftrightarrow \\ $$$$\left(\frac{{a}}{\mathrm{2}}+{b}+{c}+{d}\right)^{\mathrm{2}} +\frac{\mathrm{3}{a}^{\mathrm{2}} }{\mathrm{4}}\geqslant\mathrm{0} \\ $$$$,,=''\:{for}\:{a}=\mathrm{0};\:{b}+{c}+{d}=\mathrm{0} \\ $$
Commented by mathdanisur last updated on 16/Aug/21
$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{Ser}\:\mathrm{nice} \\ $$