Question

If x=5+2√6 then find x-1/x

Answer 1

4√6

Step-by-step explanation:

$x = 5 + 2 \sqrt{6} \\ \frac{1}{x} = \frac{1}{5 + 2 \sqrt{6} } \times \frac{5 - 2 \sqrt{6} }{5 - 2 \sqrt{6} } \\ \: \: \: \: = \frac{5 - 2 \sqrt{6} }{(5) ^{2} - (2 \sqrt{6})^{2} } \\ \: \: \: = \frac{5 - 2 \sqrt{6} }{25 - 24} \\ \: \: \: \: = 5 - 2\sqrt{6}$

Now

x-1/x=5+2√6-(5-2√6)=5+2√6-5+2√6=4√6