If $x = \frac{1}{x} = 7, $ then $x^3 +\f

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

If $x = \frac{1}{x} = 7, $ then $x^3 +\frac{1}{x^3}$ is equal to :

Options:

322

340

343

161

Correct Answer:

322

Explanation:

We know that,

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

then, $x^3 +\frac{1}{x^3}$ = n³ - 3 × n

If $x = \frac{1}{x} = 7, $

then $x^3 +\frac{1}{x^3}$ = 7³ - 3 × 7 = 343 - 21 = 322