If the lines x+my+n=0, mx+ny+ =0 and nx+ y+m=0 are concurrent then

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}-\mathrmm^{3}-\mathrmn^{3}=0 \\ (\ell+\mathrm{m}+\mathrm{n})\left(\ell^{2}+\mathrmm^{2}+\mathrmn^{2}-(\mathrm{m}-\mathrm{mn}-\mathrm{n} \ell)=0\right. \end{array} $\Rightarrow \quad \ell+$\mathrm{m}+\mathrm{n}=0 \left[\because \ell^{2}+\mathrmm^{2}+\mathrmn^{2}$ >6 \mathrm{ m}+\mathrm{mn}+\mathrm{n}\right]