Question

${ \large{ \bf{✪ \: \: If \: \: x = 2 + \sqrt{3} }}}$
${ \large{ \bf{➢ \: \: Then \: \: find \: = \:{ \bigg(} x + \dfrac{1}{x}{ \bigg) }}}}$
✔ Please solve it correctly .
✒ Don't spam, otherwise 20 answers will be reported !!​

Answer 1

Answer:

• = 4

Step-by-step explanation:

Given :

• $\sf{x = 2 + \sqrt{3} }$

To find :

• ${ \bf{ the \: value \: of \: = \:{ \bigg(} x + \dfrac{1}{x}{ \bigg) }}}$

Solution :

__________________________________________

$\\ \sf : \implies \: x + \frac{1}{x}$

$\\ \sf : \implies \: (2 + \sqrt{3} ) + \frac{1}{(2 + \sqrt{3} )}$

___________________________________

$\\ \mathbf{ Rationalise \: \: ( \frac{1}{2 + \sqrt{3}})}$

$\\ \sf : \: \longrightarrow \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} }$

$\\ \sf : \: \longrightarrow \: \frac{ 1(2 - \sqrt{3} )}{(2) {}^{2} - ( \sqrt{3} {)}^{2} }$

$\\ \sf : \: \longrightarrow \: \frac{2 - \sqrt{3} }{4 - 3}$

$\\ \sf : \: \longrightarrow {2 - \sqrt{3} }$

___________________________________

$\\ \sf : \implies(2 + \sqrt{3} ) + (2 - \sqrt{3} )$

$\\ \sf : \implies2 + 2 + \sqrt{3 } - \sqrt{3}$

$\\ \sf : \implies \boxed{ \pink{ \frak{4}}}$

__________________________________________

Therefore, the value of $\underline{\sf{x + \frac{1}{x} = 4}}$