if x=2+2^(2/3)+2^(1/3) then x^3-6x^2+6x= ? Please show the steps

Question

Aman Bansal · Answer

dear Raunak,

the answer to your question is 2

we have x-2=2^2/3-2^1/3

then cubing both sides to get,

(x-2)³= 6(x-2)

thus expnding to get,

x³-6x²+6x=2

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AMAN BANSAL

Aman Bansal · Answer

dear raunak,

I have already posted reply to your question.

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Please approve the answer...!!!!!!
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AMAN BANSAL

sona · Answer

Given that x = 2 + 2^(2/3) + 2^(1/3)

so x - 2 = 2^(2/3) + 2^(1/3)

=(x-2)^3 = [2^(2/3)+2^(1/3)]^3

using (a-b)^3= a^3 - b^3 - 3ab(a-b)

and (a+b)^3= a^3 + b^3 + 3ab(a+b) formulae.

or x^3 - 8 - 6x(x-2) = 2^2 + 2^1 + 3*[2^{(2/3)+(1/3)}[2^(2/3)+2^(1/3)

or x^3 - 8 - 6x^2 + 12x = 4 + 2 + 6(x-2)

or x^3 - 8 -6x^2 + 12x = 6 + 6x - 12

or x^3 - 6x^2 +6x = 2

Kushagra Madhukar · Answer

Dear student, Please find the attached solution to your problem. We have, x = 2 + 2 2/3 + 2 1/3 or, x – 2 = 2 2/3 + 2 1/3 cubing both sides, we get, x 3 – 8 – 6x(x – 2) = 2 2 + 2 + 3x2 3/3 (2 2/3 + 2 1/3 ) x 3 – 6x 2 + 12x – 8 = 6 + 6(x – 2) ( since, 2 2/3 + 2 1/3 = x – 2) hence, x 3 – 6x 2 + 6x = 6 + 8 -12 = 2 Hope it helps. Thanks and regards, Kushagra

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if x=2+2^(2/3)+2^(1/3) then x^3-6x^2+6x= ? Please show the steps

if x=2+2^(2/3)+2^(1/3)
then x^3-6x^2+6x= ?
Please show the steps

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