Question

if x+1/x=5, then find the value of x^3+1/x^3​

Answer 1

${x}^{3} + \frac{1}{ {x}^{3} } = 110$

Step-by-step explanation:

$x + \frac{1}{x} = 5 \\ cube \: both \: sides \\ {(x + \frac{1}{x}) }^{3} = {5}^{3} \\ {x}^{3} + \frac{1}{ {x}^{3} } + 3x \times \frac{1}{x} (x + \frac{1}{x}) = 125 \\ {x}^{3} + \frac{1}{ {x}^{3} } + 3(5) = 125 \\ {x}^{3} + \frac{1}{ {x}^{3} } +15 = 125 \\ {x}^{3} + \frac{1}{ {x}^{3} } = 110$