# If X + 1 X = 5 , Find the Value of X 3 + 1 X 3 - Mathematics

If $x + \frac{1}{x} = 5$, find the value of $x^3 + \frac{1}{x^3}$

#### Solution

In the given problem, we have to find the value of  x^3 + 1/x^3

Given  x+1/x = 5

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

Here putting, x+1/x = 5,

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

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

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

125 = x^3 + 1/x^3 + 3 xx 5 

125 = x^3 + 1/x^3 +1 5 

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

110 = x^3 + 1/x^3

Hence the value of  x^3 +1/x^3`is 110

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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 4 Algebraic Identities
Exercise 4.3 | Q 4 | Page 20