Practicing Success

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

If $ a + \frac{1}{a} = 8,$ then what is the value of $\frac{1}{a^4} +a^4 $ ?

Options:

4098

3846

3842

4094

Correct Answer:

3842

Explanation:

If $ a + \frac{1}{a} = 8,$

then what is the value of $\frac{1}{a^4} +a^4 $

If $K+\frac{1}{K}=n$

then, $K^2+\frac{1}{K^2}$ = n2 – 2

If $ a + \frac{1}{a} = 8,$

Then, $ a^2 + \frac{1}{a^2}$ =  82 – 2 = 62

And, $ a^4 + \frac{1}{a^4}$  =  622 – 2 = 3842