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Question
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 (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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