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x given as a sum of surd or root terms: isolate, square or cube, and evaluate a polynomial in x

This type of question, asked 3 times: CDS 2 2018, CDS 2 2025, CDS 2 2026. All 3 questions below, oldest first.

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  1. Question 1

    CDS 2 2018

    3
    If x=2+22/3+21/3x = 2 + 2^{2/3} + 2^{1/3}, then the value of the expression x3−6x2+6xx^3 - 6x^2 + 6x will be

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  2. Question 2

    CDS 2 2025

    23
    If x=2+21/2+23/2x=2+2^{1/2}+2^{3/2}, then what is x2−4x−10x^2-4x-10 equal to?

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  3. Question 3

    CDS 2 2026

    30
    If x=3−31/3−32/3x = 3 - 3^{1/3} - 3^{2/3}, then what is x(x−3)(x−6)x(x - 3)(x - 6) equal to ?

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