# If X = 2 3 + √ 7 ,Then (X−3)2 = - Mathematics

MCQ

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

• 1

• 3

• 6

• 7

#### 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

Concept: Laws of Exponents for Real Numbers
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 3 Rationalisation
Exercise 3.4 | Q 10 | Page 17

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