Math, asked by ibrahim909, 1 day ago

pls answer
if x=2+2^2/3+2^1/3,then find the value of x^3-6x^2+6x.​

Answers

Answered by Anonymous
0

Answer:

2

Step-by-step explanation:

x=2+2^2/3 +2^1/3  

⇒(x−2)=2^2/3 +2  ^1/3

⇒(x−2)=2 ^2/3 +2^1/3

On cubing both sides, we get

(x−2)  ^3  =2^2 +2+3⋅2^2/3 ⋅2  ^1/3 (2  ^2/3 +2 ^1/3 )  

⇒x  ^3 −6x^2 +12x−8=4+2+3×2×(x−2)  

⇒x ^3 −6x  ^2 +6x=2.

Answered by vishalnaag2018
0

Step-by-step explanation:

If x=2+2*2/3+2*1/3 what is the value of x^3-6x^2+6x?

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

use (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

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