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

Answer in Brief

If  \[x - \frac{1}{x} = 5\] ,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 = 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 -3 (x xx 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 -15 `

`125 +15=  x^3 -1 /x^3 `

`140 = x^3 -1 /x^3 `

Hence the value of  `x^3  -1 /x^3 ` is  140.

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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 4 Algebraic Identities
Exercise 4.3 | Q 6 | Page 20
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