Question

Daca x + 1/x = 5 atunci x³ + 1/x³ =??

Answer 1

              
$\frac{x-1}{x}=5 \\ \\ \frac{x}{x}- \frac{1}{x}=5 \\ \\ 1 - \frac{1}{x}=5 \\ \\\frac{-1}{x}=5-1 \\ \\ \frac{-1}{x}=4 \\ \\ 4x=-1 \\ \\ x=- \frac{1}{4}$
     
  
$=> x^{3}+ \frac{1}{ x^{3}}= (\frac{-1}{4})^{3}+ \frac{1}{ (\frac{-1}{4})^{3}}= \frac{-1}{64}+ \frac{1}{ \frac{-1}{64}}= \\ \frac{-1}{64}- \frac{64}{ 1}}=\frac{-1}{64}- \frac{64^{2}}{64}} = \frac{-1-4096}{64}= \frac{-4097}{64}$