Mathematics - Straight Lines Question with Solution | TestHub

Since the lines are concurrent, so $$\Rightarrow \begin{array}{l}\left|\begin{array}{lll}\ell & \mathrm{m}& \mathrm{n}\\ \mathrm{m}& \mathrm{n}& \ell \\ \mathrm{n}& \ell & \mathrm{m}\end{array}\right|=0\Rightarrow 3\ell \mathrm{mn}-{\ell }^3-{\mathrm{m}}^3-{\mathrm{n}}^3=0\\ (\ell +\mathrm{m}+\mathrm{n})({\ell }^2+{\mathrm{m}}^2+{\mathrm{n}}^2-(\mathrm{m}-\mathrm{mn}-\mathrm{n}\ell )=0\end{array}$$ $\Rightarrow \ell +\mathrm{m}+\mathrm{n}=0\left[\because {\ell }^2+{\mathrm{m}}^2+{\mathrm{n}}^2>6\mathrm{m}+\mathrm{mn}+\mathrm{n}\right]$