If $x+\frac{1}{x}=-2$, then what is the

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

If $x+\frac{1}{x}=-2$, then what is the value of $x^{17}+x^{-17}+x^{12}+x^{-12}$? (x < 0)

Options:

-2

-1

Correct Answer:

Explanation:

If $x+\frac{1}{x}=-2$

Then what is the value of $x^{17}+x^{-17}+x^{12}+x^{-12}$

Put x = -1

$-1^{17}+-1^{-17}+-1^{12}+-1^{-12}$ = -1 + 1 - 1 + 1 = 0