x cube + 1/x cube = 110 find the value of x + 1/x - Maths - Number Systems

Question

x cube + 1/x cube = 110
find the value of x + 1/x

Aakash Sharma · Accepted Answer

$Let x + \frac{1}{x} = y \Rightarrow (x + \frac{1}{x})^{3} = y^{3} \Rightarrow x^{3} + \frac{1}{x^{3}} + 3 (x + \frac{1}{x}) = y^{3} \Rightarrow 110 + 3 y = y^{3} \Rightarrow y^{3} - 3 y - 110 = 0 \Rightarrow (y - 5) (y^{2} + 5 y + 22) = 0$

Since for y² + 5y + 22, y does not have any real zeroes

∴ y = 5

$\Rightarrow x + \frac{1}{x} = 5$

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