Practicing Success

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

If $(k + \frac{1}{k})^2 $ = 9, then what is the value of $k^3 +\frac{1}{k^3}$ ?

Options:

27

18

15

21

Correct Answer:

18

Explanation:

If x + \(\frac{1}{x}\)  = n

then, $x^3 +\frac{1}{x^3}$ = n3 - 3 × n

If $(k + \frac{1}{k})^2 $ = 9

$(k + \frac{1}{k}) $ = 3

Then, $k^3 +\frac{1}{k^3}$ =  33 - 3 × 3 = 18