If x2 - 13x - 1= 0 and x >

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

If x² - 13x - 1= 0

and x > 1, then the value of

x³ - \(\frac{1}{x^3}\) will be:

Options:

2158

2155

2197

2345

Correct Answer:

2158

Explanation:

If x² - 13x - 1= 0

Divide by x on both sides,

x - \(\frac{1}{x}\) = 13

x³ - \(\frac{1}{x^3}\) = 13³ + 3 × 13 = 2158

Note - if x - \(\frac{1}{x}\) = a

then x³ - \(\frac{1}{x^3}\) = a³ + 3a