If $x + \frac{1}{x} = -13$, what is the

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

If $x + \frac{1}{x} = -13$, what is the value of $x^4 +\frac{1}{x^4}$ ?

Options:

27887

27891

29243

28561

Correct Answer:

27887

Explanation:

We know that,

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

then, $K^2+\frac{1}{K^2}$ = n² – 2

So,

If $x + \frac{1}{x} = -13$,

= $x^2 +\frac{1}{x^2}$ = 13² – 2 = 167

The value of $x^4 +\frac{1}{x^4}$ = 167² – 2 = 27887