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Question
If x = \[\frac{2}{3 + \sqrt{7}}\],then (x−3)2 =
Options
1
3
6
7
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Solution
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`
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