Question

If $x=5-2\sqrt{6}$ find $x^2+\frac{1}{x^2}$

Answer 1

Given $x=5-2\sqrt{6}$

Now $x^2+\frac{1}{x^2}=(5-2\sqrt{6}{)}^2+\frac{1}{(5-2\sqrt{6}{)}^2}$

=$(49-20\sqrt{6})+\frac{1}{(49-20\sqrt{6})}$

=$(49-20\sqrt{6})+\frac{(49+20\sqrt{6})}{(49-20\sqrt{6})\times (49+20\sqrt{6})}$

=$(49-20\sqrt{6})+\frac{(49+20\sqrt{6})}{(2401-2400)}$

=$(49-20\sqrt{6})+\frac{(49+20\sqrt{6})}{\left(1\right)}$

=$98$