# If X 3 + 1 X 3 = 110 , Then X + 1 X = - Mathematics

MCQ

If $x^3 + \frac{1}{x^3} = 110$, then $x + \frac{1}{x} =$

#### Options

• 5

• 10

• 15

• none of these

#### Solution

In the given problem, we have to find the value of  x + 1/x

Given  x^3 + 1/x^3 = 110

We shall use the identity (a + b)^3 = a^3 + b^3 + 3ab (a+b)

(x+1/x)^3 = x^3 + 1/x^3 + 3 xx x xx 1/x(x+ 1/x)

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

Put  x + 1/x = ywe get,

(y)^3 = x^3 + 1/x^3 + 3 (y)

Substitute y = 5 in the above equation we get

(5)^3 = x^3 + 1/x^3 + 3(5)

125 = x^3 + 1/x^3 + 15

125 - 15 = x^3 + 1/x^3

110 = x^3 + 1/x^3

The Equation (y)^3 = x^3 + 1/x^3 + 3(y) satisfy the condition that  x^3 + 1/x^3 = 110

Hence the value of  x+ 1/x is 5.

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 4 Algebraic Identities
Q 6 | Page 30