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A Problem Of IMO

Please help me.

If x = \(2 + \sqrt[3]{2} + \sqrt[3]{2^2}\), Then \(x^3 - 6x^2 + 6x\) = ?

Note by Swapnil Das
2 years, 3 months ago

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Take 2 on LHS and cube on both the sides

\(\displaystyle (x-2)^3 = 2(1 + 2^{\frac{1}{3}})^3\)

Simplifing

\(\displaystyle x^3 -6x^2 + 12x - 8 = 6(1 + 2^{\frac{1}{3}} + 2^{\frac{2}{3}})\)

Rearranging (formation of x on RHS)

\(\displaystyle x^3 -6x^2 + 12x -8 = 6x -6\)

\(\displaystyle x^3 - 6x^2 + 6x = 2\) Krishna Sharma · 2 years, 3 months ago

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@Krishna Sharma Can U please recommend me some books for trigonometry? Swapnil Das · 2 years, 3 months ago

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@Swapnil Das I never read any Trigonometry books but I am sure Omkar kulkarni can help you out(I am unable to tag him right now) Krishna Sharma · 2 years, 3 months ago

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@Krishna Sharma Thanks for suggestion! Swapnil Das · 2 years, 3 months ago

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@Krishna Sharma Thank You. You were really helpful! Swapnil Das · 2 years, 3 months ago

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x=2 Jacob Johanssen · 2 years, 2 months ago

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