Question

if x = 4+√2, find x+1/x​

Answer 1

EXPLANATION.

⇒ x = 4 + √2.

As we know that,

We can write equation as,

⇒ 1/x = 1/(4 + √2).

Rationalizes the denominator, we get.

⇒ 1/x = 1/(4 + √2) x (4 - √2)/(4 - √2).

⇒ 1/x = (4 - √2)/[(4 + √2)(4 - √2)].

⇒ 1/x = (4 - √2)/[(4)² - (√2)²].

⇒ 1/x = (4 - √2)/[16 - 2].

⇒ 1/x = (4 - √2)/(14).

To find : (x + 1/x).

⇒ x + 1/x = (4 + √2) + [(4 - √2)/14].

⇒ x + 1/x = [14(4 + √2) + (4 - √2)/(14)].

⇒ x + 1/x = [56 + 14√2 + 4 - √2]/(14).

⇒ x + 1/x = [(60 + 13√2)/14].

Answer 2

$\mathfrak{ the \: \: \: value \: \: \: of \: \: \boxed{ \pink{\sf x + \frac{1}{x} } }\: \: \: is \: \: }$

$\boxed{ \large \sf \orange {\: \frac{60 - 13 \sqrt{2} }{14} }}$

Explanation :

For Further Explanation, refer the given attachment