Question

If p= 5+2 root 6 and x=1 by p, then what will be the value of p square + x square ?

Answer 1

$$\begin{gathered} \mathrm{p}=5+2\sqrt{6} \\ \mathrm{Now},\mathrm{x}=\frac{1}{\mathrm{p}}=\frac{1}{5+2\sqrt{6}}=\frac{1}{5+2\sqrt{6}}\times \frac{5-2\sqrt{6}}{5-2\sqrt{6}}=5-2\sqrt{6} \\ \mathrm{Now},{\mathrm{p}}^2+{\mathrm{x}}^2={\left(5+2\sqrt{6}\right)}^2+{\left(5-2\sqrt{6}\right)}^2 \\ =25+24+20\sqrt{6}+25+24-20\sqrt{6} \\ =98 \end{gathered}$$