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Question
If \[x^3 + \frac{1}{x^3} = 110\], then \[x + \frac{1}{x} =\]
Options
5
10
15
none of these
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Solution
In the given problem, we have to find the value of `x + 1/x`
Given `x^3 + 1/x^3 = 110`
We shall use the identity `(a + b)^3 = a^3 + b^3 + 3ab (a+b)`
`(x+1/x)^3 = x^3 + 1/x^3 + 3 xx x xx 1/x(x+ 1/x)`
`(x+1/x)^3 = x^3 + 1/x^3 + 3 (x+ 1/x)`
Put `x + 1/x = y`we get,
`(y)^3 = x^3 + 1/x^3 + 3 (y)`
Substitute y = 5 in the above equation we get
`(5)^3 = x^3 + 1/x^3 + 3(5)`
`125 = x^3 + 1/x^3 + 15`
`125 - 15 = x^3 + 1/x^3`
`110 = x^3 + 1/x^3`
The Equation `(y)^3 = x^3 + 1/x^3 + 3(y)` satisfy the condition that `x^3 + 1/x^3 = 110`
Hence the value of `x+ 1/x` is 5.
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