Question

if x=5+2root6 then find x+1/x​

Answer 1

EXPLANATION.

⇒ x = 5 + 2√6.

As we know that,

We can write equation as,

⇒ 1/x = 1/[5 + 2√6].

Rationalize the equation, we get.

⇒ 1/x = 1/[5 + 2√6] x [5 - 2√6]/[5 - 2√6].

⇒ 1/x = [5 - 2√6]/[(5)² - (2√6)²].

⇒ 1/x = [5 - 2√6]/[25 - 24].

⇒ 1/x = [5 - 2√6].

To find :

Value of (x + 1/x).

Put the values in the equation, we get.

⇒ (x + 1/x) = [5 + 2√6 + 5 - 2√6].

⇒ (x + 1/x) = 10.

Answer 2

Topic :-

• Calculation of Rational Numbers

Question :-

• $\rm{if \: x = 5+ 2 \sqrt{6}\: then \: find \: x + \frac{1}{x}}$

Solution :-

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

By Rationalising

$\: \: \: \: \: \: \large{ \frac{1}{x} = \frac{1}{ \red{5 + 2 \sqrt{6} }} \times \frac{5 - 2 \sqrt{6} }{ \red{5 - 2 \sqrt{6} }} }$

As we know a² - b² = (a+b) (a-b)

$\: \: \: \: \frac{1}{x} = \large{\frac{5 - 2 \sqrt{6} }{(5) {}^{2} - (2 \sqrt{6} ) {}^{2} } } \\ \: \: \: \: \frac{1}{x} = \large{ \frac{5 - 2 \sqrt{6} }{25 - 24} } \\ \hookrightarrow \boxed{ \frac{1}{x} = 5 - 2 \sqrt{6} }$

Put value of x and 1/x in x + 1/x

$\: \: \: \: \: \: : \: \rightarrow \red{x + \frac{1}{x} } \\ \implies \large \: 5 + \cancel{2 \sqrt{6}} + 5 - \cancel{ 2 \sqrt{6} } \\ \implies \large{5 + 5} \\ \hookrightarrow \boxed{\underline{ \green{\huge{10}}}}$