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Question
If \[x + \frac{1}{x} = 2\], then \[x^3 + \frac{1}{x^3} =\]
Options
64
14
8
2
Solution
In the given problem, we have to find the value of `x^3+1/x^3`
Given `x+ 1/x = 2`
We shall use the identity `(a+b)^3 = a^3 +b^3 + 3ab(a+b)`
Here putting `x+ 1/x = 2`,
`(x+ 1/x)^3 = x^3 + 1/x^3 + 3 (x xx 1/x)(x+1/ x)`
`(2)^3 = x^3 + 1/x^3 + 3 (x xx 1/x )(2)`
` 8 =x^3 + 1/x^3 + 6`
` 8-6 = x^3 + 1/x^3`
` 2= x^3 + 1/x^3`
Hence the value of `x^3 + 1/x^3` is 2.
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