Question

If x = 3-✓8 then ( x + 1/x ) equals to ...................​

Answer 1

Step-by-step explanation:

$x = 3 - \sqrt{8}$

$\bigg(3 - \sqrt{8} + \frac{1}{3 - \sqrt{8} } \bigg)$

$\: \: \: \mapsto \sf{ \frac{ 3(3 - \sqrt{8} ) - \sqrt{8} (3 - \sqrt{8} ) + 1}{3 - \sqrt{8} }}$

$\: \: \: \: \implies \sf{ \frac{(9 - 3 \sqrt{8} - 3 \sqrt{8} + 8) + 1}{3 - \sqrt{8} }}$

$\: \: \: \: \implies \sf{ \frac{18 - 6 \sqrt{8} }{3 - \sqrt{8} } } \: is \: the \: answer$

Answer 2

Given :

• x = 3 - √8

To find :

• x + 1/x

According to the question,

$\sf \implies {\dfrac{1}{x} = \dfrac{1}{ 3 - \sqrt{8} } \times \dfrac{3 + \sqrt{8} }{3 + \sqrt{8} } } \\ \\ \implies \sf{ \frac{3 + \sqrt{8} }{9 - 8} } \\ \\ \implies \sf{3 + \sqrt{8} } \green \bigstar$

$\implies \sf{x + \dfrac{1}{ x } } \\ \\ \implies \sf{3 - \cancel{\sqrt{8} } + 3 + \cancel{\sqrt{8} }} \\ \\ \implies \sf{6} \green \bigstar$

So,the value of x + 1/x is 6...