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Question

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

This question was previously asked in
CDS 2 2026 Maths Question Paper (13-Sep-2026)
The correct answer is

-12

Let \(t=3^{1/3}\), so \(t^3=3\) and \(x=3-t-t^2\). Using \(t^3=3\) and \(t^4=3t\), expansion gives \(x^2=15-3t-5t^2\) and \(x^3=69-9t-27t^2\). Then \(x(x-3)(x-6)=x^3-9x^2+18x=(69-9t-27t^2)-9(15-3t-5t^2)+18(3-t-t^2)=-12\), since all terms in \(t\) and \(t^2\) cancel out.

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Important Questions from Cubes & Cube Roots

  1. What is the simplified value of \(\dfrac{(0.25)^3 + (0.05)^3}{(0.5)^3 + (0.1)^3}\)?

  2. What is the simplified value of \(\dfrac{(0.05)^3 + (0.005)^3}{(0.25)^3 + (0.025)^3}\)?

  3. If $11 \rightarrow 1331, 12 \rightarrow 1728$, then $13 \rightarrow ?$
  4. A gardener organizes plants into rows to create a square formation but discovers that 15 plants are not included. If the total number of plants is 3984, then what is the number of plants in each row?

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