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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 \[x^3 - \frac{1}{x^3}\]

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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 .

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APPEARS IN

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