Question

${x}^{3} + ( \frac{1}{x})^{3} = 110$
then find
$x + \frac{1}{x} =$

Answer 1

Solution:-
It's given that,
${x}^{3} + { (\frac{1}{x} )}^{3} = 110$
$(x + { \frac{1}{x} })^{3} - 3(x + \frac{1}{x} ) = 110$
$let \: (x + \frac{1}{x}) \: be \: m$
So,
${m}^{3} - 3m - 110 = 0 \\ m( {m}^{2} - 3) = 110$
Now,
$m ({m}^{2} - 3) = 5( {5}^{2} - 3)$
Hence,
K=5