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

Aman Bansal
592 Points
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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AMAN BANSAL

Aman Bansal
592 Points
10 years ago

dear raunak,

BEST OF LUCK

Now you can win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.
AMAN BANSAL

sona
19 Points
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

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