Question

If x = 1 – √2, then the value of x + 1/x





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Answer 1

Answer:

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Answer 2

❄ GIVEN :-

x = 1 - √2

❄ SOLUTION ❄

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

$= (1 - \sqrt{2}) + ( \frac{1}{1 - \sqrt{2} } )$

$= \frac{(1 - \sqrt{2})(1 - \sqrt{2}) + 1 }{(1 - \sqrt{2} )}$

$= \frac{(1 - \sqrt{2} ) ^{2} + 1}{1 - \sqrt{2} }$

$= \frac{1 + 2 - 2 \times 1 \times \sqrt{2} + 1}{1 - \sqrt{2} }$

$= \frac{ 4 - 2 \sqrt{2} }{1 - \sqrt{2} }$

$= \frac{(4 - 2 \sqrt{2} )}{(1 - \sqrt{2} )} \times \frac{(1 + \sqrt{2} )}{(1 + \sqrt{2} )}$

on multiplying...

$= \frac{(4 + 4 \sqrt{2} - 2 \sqrt{2} - 2 \times 2)}{ {(1)}^{2} - { (\sqrt{2} )}^{2} }$

$= \frac{(4 - 4 + 2 \sqrt{2} )}{(1 - 2)}$

$= \frac{(2 \sqrt{2}) }{( - 1)}$

$= - 2 \sqrt{2}$

Answer___

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