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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

Grade:11

4 Answers

Aman Bansal
592 Points
9 years ago

dear Raunak,

the answer to your question is 2

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

BEST OF LUCK

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AMAN BANSAL

Aman Bansal
592 Points
9 years ago

dear raunak,

I have already posted reply to your question.

BEST OF LUCK

Please approve the answer...!!!!!!
We are all IITians and here to help you in your IIT JEE preparation.
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.
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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

Kushagra Madhukar
askIITians Faculty 629 Points
9 months ago
Dear student,
Please find the attached solution to your problem.
 
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

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