Question

If x= \[\sqrt{2} - 1\], then write the value of \[\frac{1}{x} . \]

Answer 1

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`.