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

10 years ago

dear Raunak,

we have x-2=22/3-21/3

then cubing both sides to get,

(x-2)3= 6(x-2)

thus expnding to get,

x3-6x2+6x=2

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10 years ago

dear raunak,

BEST OF LUCK

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AMAN BANSAL

3 years ago

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
one year ago
Dear student,

We have, x = 2 + 22/3 + 21/3
or, x – 2 = 22/3 + 21/3
cubing both sides, we get,
x3 – 8 – 6x(x – 2) = 22 + 2 + 3x23/3(22/3 + 21/3)
x3 – 6x2 + 12x – 8 = 6 + 6(x – 2)                     ( since, 22/3 + 21/3 = x – 2)
hence, x3 – 6x2 + 6x = 6 + 8 -12 = 2

Hope it helps.
Thanks and regards,
Kushagra