Question

if a is
$5 + 2 \sqrt{6} \: then \: find \: the \: value \: of \: \: a + \frac{1}{a}$
​

Answer 1

Step-by-step explanation:

solution:-

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

we have find

$a + \frac{1}{a}$

so value of a is given then put the value of a

$5 + 2 \sqrt{6} + \frac{1}{5 + 2 \sqrt{6} }$

now take a lcm

$\frac{(5 + 2 \sqrt{6} )(5 + 2 \sqrt{6}) + 1 }{5 + 2 \sqrt{6} } \\ \frac{(5 + 2 \sqrt{6} ) { }^{2} + 1}{5 + 2 \sqrt{6} } \\ \frac{5 {}^{2} + (2 \sqrt{6} ) {}^{2} + 5 \times 2 \times 2 \sqrt{6} + 1}{5 + 2 \sqrt{6} } \\ \frac{25 + 24 + 20 \sqrt{6} + 1}{5 + 2 \sqrt{6} } \\ \frac{50 + 20 \sqrt{6} }{5 + 2 \sqrt{6} }$

take 10 common from nominator

$\frac{10 (5 + 2 \sqrt{6} )}{5 + 2 \sqrt{6} } \\ 5 + 2 \sqrt{6} \: is \: same \: so \: it \: cancle \: out \\ \implies10$

ANSWER:- 10