Question

If $x=5-2\sqrt{6},$ find the value of :${(x-\frac{1}{x})}^2$

Answer 1

Now $\frac{1}{x}=5+2\sqrt{6}$

Thus the value of $(x-\frac{1}{x}{)}^2$ $=$((5 - 2$\sqrt{6}$) - (5 + 2$\sqrt{6})$)${}^2$ $=$(4\sqrt{6})^2= $16\times 6$ $=$ $96$

Thus the correct answer is $96$.