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

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16 votes

Answer:

Value is 3 - √8

Explanation:

$x = 3 + √(8) \\ \\ (1)/(x) = (1)/(3 + √(8) ) \\$

rationalise the denominator:

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

Brielle answered Aug 24, 2022

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