Advertisement Remove all ads

# If X − 1 X = 7 ,Find the Value of X 3 − 1 X 3 - Mathematics

Answer in Brief

If $x - \frac{1}{x} = 7$ ,find the value of $x^3 - \frac{1}{x^3}$

Advertisement Remove all ads

#### Solution

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

Given  x- 1/x = 7

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

Here putting,  x- 1/x = 7,

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

(7)^3 = x^3 - 1/x^3 - 3 (x xx 1/x ) (x-1/x)

 343 = x^3 - 1/x^3 -3 (x - 1/x)

 343 = x^3 - 1/x^3 -3 xx 7

 343 = x^3 - 1/x^3  - 21

 343 + 21 = x^3 - 1/x^3

 343  = x^3 - 1/x^3

Hence the value of  x^3 - 1/x^3 is  364 .

Is there an error in this question or solution?
Advertisement Remove all ads

#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 4 Algebraic Identities
Exercise 4.3 | Q 5 | Page 20
Advertisement Remove all ads

#### Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications

Forgot password?
Course