Flag Algebra> Simple Quadratic...
question mark

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

raunak samanta , 14 Years ago
Grade 11
anser 4 Answers
Aman Bansal

Last Activity: 14 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

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.
Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar : Click here to download the toolbar..  
AMAN BANSAL

Aman Bansal

Last Activity: 14 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.
Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar : Click here to download the toolbar..  
AMAN BANSAL

sona

Last Activity: 7 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

Last Activity: 4 Years 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

star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments