Question

if x+1/x=2, then x^3+1 /x^3=?????

Answer 1

We have,
$x + \frac{1}{x} = 2$
Then, we know that,
$( {x}^{3} + \frac{1}{ {x}^{3} } ) = {(x + \frac{1}{x} )}^{3} - 3(x + \frac{1}{x} ) \\ \: \\ = > {2}^{3} - 3 \times 2 = 2$
Hence, our answer is 2 .