# If X = 3 √ 2 + √ 3 , Then X 3 + 1 X 3 = - Mathematics

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads
MCQ

If x = $\sqrt[3]{2 + \sqrt{3}}$ , then $x^3 + \frac{1}{x^3} =$

#### Options

• 2

• 4

• 8

• 9

Advertisement Remove all ads

#### Solution

Given that . x = 3sqrt(2+sqrt3) It can be simplified as

 x^3 =  2+sqrt3

1/ x^3 = 1 /(2+sqrt3)

We know that rationalization factor for 2+sqrt3 is 2- sqrt3. We will multiply numerator and denominator of the given expression  1/(2+sqrt3)by 2-sqrt3, to get

1/x^3 = 1/(2+sqrt3 )  xx (2-sqrt3)/(2-sqrt3)

= (2-sqrt3)/((2)^2 - (sqrt3)^2)

= (2-sqrt3)/(4-3)

=2-sqrt3

Therefore,

x^3 + 1/x^3 = 2 +sqrt3 +2 - sqrt3

= 2+2

=4

Concept: Laws of Exponents for Real Numbers
Is there an error in this question or solution?
Chapter 3: Rationalisation - Exercise 3.4 [Page 17]

#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 3 Rationalisation
Exercise 3.4 | Q 18 | Page 17

#### Video TutorialsVIEW ALL [1]

Share
Notifications

View all notifications

Forgot password?