# If X + √ 15 = 4 , Then X + 1 X = - Mathematics

MCQ

If $x + \sqrt{15} = 4,$ then $x + \frac{1}{x}$ =

• 2

• 4

• 8

• 1

#### Solution

Given that .x+sqrt15 = 4 It can be simplified as

 x =4 -sqrt15

1/x = 1/(4-sqrt15)

We need to find  x+1/x

We know that rationalization factor for 4-sqrt15  is 4 +sqrt15. We will multiply numerator and denominator of the given expression 1/(4-sqrt15)by , 4+sqrt15 to get

1/x = 1/(4-sqrt15) xx (4+sqrt15)/ (4+sqrt15)

= (4+sqrt15)/((4^2) - (sqrt15)^2)

= (4+sqrt15)/(16-15)

= 4+sqrt15

Therefore,

x +1/x = 4 - sqrt15 + 4 + sqrt15

 = 4+ 4

=  8

Concept: Laws of Exponents for Real Numbers
Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 3 Rationalisation
Exercise 3.4 | Q 12 | Page 17

Share