If x1001 + \(\frac{1}{x^{1001}}\) =

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

If x¹⁰⁰¹ + \(\frac{1}{x^{1001}}\) = 15

Find x¹⁰⁰¹ - \(\frac{1}{x^{1001}}\) = ?

Options:

\(\sqrt {229}\)

\(\sqrt {233}\)

\(\sqrt {221}\)

\(\sqrt {227}\)

Correct Answer:

\(\sqrt {221}\)

Explanation:

Formula → If x + \(\frac{1}{x}\) = a

Then, x - \(\frac{1}{x}\) = \(\sqrt {a^2 - 4}\)

Given, x¹⁰⁰¹ + \(\frac{1}{x^{1001}}\) = 15

So, x¹⁰⁰¹ - \(\frac{1}{x^{1001}}\) = \(\sqrt {(15)^2 - 4}\) = \(\sqrt {221}\)