Question

if a=5-2root 6 find the value of root a-1/root a​

Answer 1

$a = 5 - 2 \sqrt{6} \\ \frac{1}{a } = \frac{1}{5 - 2 \sqrt{6 } } \\ \frac{1}{5 - 2 \sqrt{6} } \times \frac{5 + 2 \sqrt{6} }{5 + 2 \sqrt{6} } \\ \frac{5 + 2 \sqrt{6} }{ {5}^{2} - ( {2 \sqrt{6} })^{2} } \\ \frac{5 + 2 \sqrt{6} }{1} \\ 5 + 2 \sqrt{6} \\ 5 - 2 \sqrt{6} - (5 + 2 \sqrt{6) } =-4 \sqrt{6}$