# If X = √ 5 + 2 ,Then X − 1 X Equals - Mathematics

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MCQ

If x = $\sqrt{5} + 2$,then $x - \frac{1}{x}$ equals

#### Options

• $2\sqrt{5}$

• 4

• 2

• $\sqrt{5}$

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#### Solution

Given that. x=sqrt5 +2  Hence  1/xis given as

1/x = 1/(sqrt5+2).We need to find  x - 1/x

We know that rationalization factor for sqrt5+2 issqrt5-2. We will multiply numerator and denominator of the given expression\1/(sqrt5 +2) bysqrt5 - 2, to get

1/x = 1/(sqrt5+2 ) xx (sqrt5 - 2)/(sqrt5 -2)

 = (sqrt 5-2)/((sqrt5)^2 - (2)^2 )

=(sqrt5 -2)/(5-4)

 = sqrt5 - 2

Therefore,

x - 1/x=sqrt5 +2 -(sqrt5 - 2)

= sqrt5 +2 - sqrt5 +2

 = 2+2

 = 4

Concept: Operations on Real Numbers
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 3 Rationalisation
Exercise 3.4 | Q 5 | Page 17

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