Question

if
$x + \frac{1}{x}$=9
find the value of
${x}^{3} + \frac{1}{x {}^{3} }$
pls solve this one immediately

Answer 1

$\: (x + \frac{1}{x} ) {}^{3} = {x}^{3} + {( \frac{1}{x} )}^{3} + 3 \times x \times \frac{1}{x} (x + \frac{1}{x} ) \\ \\ \: \: \: \: \: \: \: \: \: \: {(9)}^{3} = {x}^{3} + \frac{1}{x {}^{3} } + 3(9) \\ \\ \: \: \: \: \: \: \: \: \: \: 729 = {x}^{3} + \frac{1}{x {}^{3} } + 27 \\ \\ 729 - 27 = {x}^{3} + \frac{1}{x {}^{3} } \\ \\ \: \: \: \: \: \: \: \: \: \: 702 = {x}^{3} + \frac{1}{x {}^{3} }$