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Question
If x= \[\sqrt{2} - 1\], then write the value of \[\frac{1}{x} . \]
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Solution
Given that. `x= sqrt2-1 ` Hence `1/x`is given as
`1/x = 1/(sqrt2-1)`
We know that rationalization factor for `sqrt2-1`is `sqrt2+1` . We will multiply each side of the given expression `1/(sqrt2-1)`by, `sqrt2+1` to get
`1/(sqrt2-1) xx (sqrt2+1)/(sqrt2+1) = (sqrt2+1)/((sqrt2)^2 - (1)^2)`
` = (sqrt2 +1)/(2-1)`
`= sqrt2 +1`
Hence the value of the given expression is`sqrt2 +1`.
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