If $y+\frac{1}{y}= 11$, then the value of $y^3-\frac{1}{y^3}$ is:
Answer & explanation
Correct answer: option 2
If $y+\frac{1}{y}= 11$
then $y+\frac{1}{y}$ = \(\sqrt {11^2 - 4}\)
= $y+\frac{1}{y}$ = 3\(\sqrt {13}\)
$y^3-\frac{1}{y^3}$ = (3\(\sqrt {13}\))3 + 3 × 3\(\sqrt {13}\)
= $y^3-\frac{1}{y^3}$ = $360\sqrt{13}$