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if x=2+2^2/3+2^1/3,then find the value of x^3-6x^2+6x.
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Answer:
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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.
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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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