Question

if x = 3+root8 find the value of :- 1/x

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Answer 1

Answer:

Value is 3 - √8

Step-by-step explanation:

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

rationalise the denominator:

$= \frac{1}{3 + \sqrt{8} } . \frac{3 - \sqrt{8} }{3 - \sqrt{8} } \\ \\ = \frac{3 - \sqrt{8} }{ {3}^{2} - {( \sqrt{8}) }^{2} } \\ \\ = \frac{3 - \sqrt{8} }{9 - 8} \\ \\ = 3 - \sqrt{8}$