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Sum or difference of cubes of two numbers from their sum (or difference) and product

This type of question, asked 3 times: CDS 1 2017, CDS 1 2022, CDS 2 2025. All 4 questions below, oldest first.

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  1. Question 1

    CDS 1 2017

    33
    If a+b=5a + b = 5 and ab=6ab = 6, then what is the value of a3+b3a^3 + b^3 ?

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  2. Question 2

    CDS 1 2017

    18
    If a3=335+b3a^3 = 335 + b^3 and a=5+ba = 5 + b, then what is the value of a+ba + b (given that a>0a > 0 and b>0b > 0) ?

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  3. Question 3

    CDS 1 2022

    26
    If a+b=2,1a+1b=2a + b = 2,\quad \frac{1}{a} + \frac{1}{b} = 2 then what is the value of a3+b3a^3 + b^3 ?

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  4. Question 4

    CDS 2 2025

    7
    If 1a+1b=56\frac{1}{a}+\frac{1}{b}=\frac{5}{6} and 1a2+1b2=1336\frac{1}{a^2}+\frac{1}{b^2}=\frac{13}{36}, then what is 1a3+1b3\frac{1}{a^3}+\frac{1}{b^3} equal to?

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