Practicing Success

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

If $x+\frac{1}{x}=4$, then the value of $x^4 +(\frac{1}{x})^4$ is :

Options:

14

196

16

194

Correct Answer:

194

Explanation:

$(x - \frac{1}{x}) = a$

(x2 + x-2) = (a)2 + 2 = b

= (x4 + x-4) = b2 - 2

If $x+\frac{1}{x}=4$,

(x2 + x-2) = (4)2 - 2 = 14

then the value of $x^4 +(\frac{1}{x})^4$ is = (14)2 - 2 = 194