Question Number 223700 by BaliramKumar last updated on 02/Aug/25
$$\:\underline{\underbrace{\:}} \\ $$
Answered by mehdee7396 last updated on 02/Aug/25
$${let}\:\:{a}=\mathrm{2}{k}+\mathrm{1}\Rightarrow{x}^{\mathrm{2}} −\mathrm{2}{kx}+\mathrm{8}{k}+\mathrm{11}=\mathrm{0} \\ $$$$\Rightarrow\Delta={k}^{\mathrm{2}} −\mathrm{8}{k}−\mathrm{11}={n}^{\mathrm{2}} \\ $$$$\Rightarrow\left({k}−\mathrm{4}\right)^{\mathrm{2}} ={n}^{\mathrm{2}} +\mathrm{27}\Rightarrow{if}\:\:{n}=\mathrm{3}\Rightarrow{k}=\mathrm{10}\Rightarrow{a}=\mathrm{21} \\ $$$$ \\ $$