Question

If x = \[\frac{2}{3 + \sqrt{7}}\],then (x−3)² =

Options

• 1

• 3

• 6

• 7

Answer 1

Given that: `x=2/(3+sqrt7)`

We know that rationalization factor for `3+sqrt7` is .`3-sqrt7` We will multiply numerator and denominator of the given expression `2/(3+sqrt7)` by `3 - sqrt7`, to get

`x = 2/(3+sqrt7) xx (3-sqrt7)/ (3-sqrt7)`

`= (2(3-sqrt7))/((3)^2 - (sqrt7)^2)`

`=  (2(3-sqrt7))/(9-7) `

`= 3 - sqrt7`

Therefore,

`x-3 =-sqrt7`

On squaring both sides, we get

 `(x-3)^2 = 7`