PYQ Vault

Given x +- 1/x (or a power of it), find another power x^n +- 1/x^n

This type of question, asked 5 times: CDS 1 2018, CDS 1 2020, CDS 1 2021, CDS 2 2025, CDS 1 2026. All 5 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 1 2018

    9
    If a2−1a=5\frac{a^2 - 1}{a} = 5, then what is the value of a6−1a3\frac{a^6 - 1}{a^3}?

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  2. Question 2

    CDS 1 2020

    50
    If (x8+1x8)=47\left(x^8 + \frac{1}{x^8}\right) = 47, what is the value of (x6+1x6)\left(x^6 + \frac{1}{x^6}\right)?

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  3. Question 3

    CDS 1 2021

    22
    If x+1x=52x + \frac{1}{x} = \frac{5}{2}, then what is x4−1x4x^4 - \frac{1}{x^4} equal to?

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  4. Question 4

    CDS 2 2025

    26
    If x−1x=2x-\frac{1}{x}=2, x>0x>0; then what is x2−1x2x^2-\frac{1}{x^2} equal to?

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  5. Question 5 (case study, 2 parts)

    CDS 1 2026

    For the next two (02) items that follow : 16(x4+1x4)−257=016\left(x^4 + \frac{1}{x^4}\right) - 257 = 0
    83
    What is (x2+1x2)\left(x^2 + \frac{1}{x^2}\right) equal to ?

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    84
    What is (x3+1x3)\left(x^3 + \frac{1}{x^3}\right) equal to ?

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