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Polynomials

If [x=3+3∧1 /...

Question

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

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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 + 33^2/33^1/3(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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Similar questions

x = 3 + 3^{1 / 3} + 3^{2 / 3}

x^{3} - 9 x^{2} + 18 x - 12

=

x = 3 + 3^{\frac{1}{2}} + 3^{\frac{2}{3}}

x^{3} - 9 x^{2} + 18 x - 12

x = 3 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}}

, then find the value of

x^{3} - 9 x^{2} + 18 x

x = 2 + 2^{\frac{2}{3}} + 2^{\frac{1}{3}}

then prove that

x^{3} - 6 x^{2} + 6 x - 2 = 0

y = x^{4} + x^{3} - 18 x^{2} + 24 x - 12

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