Practicing Success

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

If $y+\frac{1}{y}= 11$, then the value of $y^3-\frac{1}{y^3}$ is:

Options:

$345\sqrt{13}$

$360\sqrt{13}$

$352\sqrt{13}$

$368\sqrt{13}$

Correct Answer:

$360\sqrt{13}$

Explanation:

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\(\sqrt {13}\)

= $y^3-\frac{1}{y^3}$ = $360\sqrt{13}$