Question

If 1/x = 3 - √8 the the value of x + 1/x is​

Answer 1

Answer:

The ansqer is 6

Step-by-step explanation:

Given ,

$\frac{1}{x} = 3 - \sqrt{8}$

So ,

$x = \frac{ \frac{1}{1} }{x} = \frac{ \frac{1}{1} }{3 - \sqrt{8} } = \frac{1}{3 - \sqrt{8} }$

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

$x = \frac{3 + \sqrt{8} }{ {3}^{2} - { \sqrt{8} }^{2} } = \frac{3 + \sqrt{8} }{9 - 8} = 3 + \sqrt{8}$

Thus ,

$x + \frac{1}{x} = 3 + \sqrt{8} + 3 - \sqrt{8}$

$x + \frac{1}{x} = 6$

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