Question

x=5+2√6 then x+1/x=
find the​

Answer 1

Given -

$x = 5 + 2 \sqrt{6}$

To find -

$x + \frac{1}{x}$=?

Solution -

$\implies x = 5 + 2 \sqrt{6}$

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

By rationalising the denominator we will get -

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

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

$\implies \frac{1}{x} = \frac{5 - 2 \sqrt{6} }{25 - 24}$

$\implies \frac{1}{x} = \frac{5 - 2 \sqrt{6} }{1}$

$\implies \frac{1}{x} = 5 - 2 \sqrt{6}$

Now,

$= x + \frac{1}{x}$

Putting the values we will get -

$= 5 + 2 \sqrt{6} + 5 - 2 \sqrt{6}$

$= 5 + 5$

$= 10$

Therefore the value of $x+\frac{1}{x}$ is 10