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Question

If [x=3+3^(1/3)+3^(2/3)] , then prove that [(x^3)-(9x^2)+18x-12]=0


Solution

  x – 3 = 3^2/3 + 3^1/3
(x – 3)^3 = (3^2/3 + 3^1/3)^3
x^3 – 27 + 27x – 9x^2 = 9 + 3 + 3*3^2/3*3^1/3(3^2/3 + 3^1/3)
x^3 – 27 + 27x – 9x^2 = 12 + 9( x – 3)
x^3 – 9x^2 + 18x – 27 = 12 – 27
x^3 – 9x^2 + 18x – 12 = 0

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