Practicing Success

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

If $k+\frac{1}{k}=4$, then what is the value of $k^4+\frac{1}{k^4}$?

Options:

410

192

212

194

Correct Answer:

194

Explanation:

If $(x + \frac{1}{x}) = n$

Then,  (x2 + x-2) = (n)2 - 2 = b

and  (x4 + x-4) = b2 - 2

If $k+\frac{1}{k}=4$

Then,  (k2 + k-2) = (4)2 - 2 = 14

(k4 + k-4) = 142 - 2 = 194