Latest self Aptitude Question SOLUTION: If x=2-2^1/3 +2^2/3, then the value of x^3 - 6x^2 +18x +18 is

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(#M40010614) SELF question Keep an EYE

If x=2-2^1/3 +2^2/3, then the value of x^3 - 6x^2 +18x +18 is

Arjun (11 years ago)

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SDeep Bhattacharya  (11 years ago)

x^3 - 6x^2 +18x +18 = [x^3 + 3*(x^2)*(-2) + 3*(x)*{(-2)^2} + (-2)^3 ] + 6x + 26
= (x-2)^3 + 6x + 26..........[(eqn1)]
Now, from the given data x-2 = [2^(2/3)- 2^(1/3)]
=> (x-2) = {2^(1/3)}[2^(1/3)- 1]
=> (x-2)^3 = [{2^(1/3)}^(3)][2^(1/3)- 1]^3
=> (x-2)^3 = 2[2+ {3*(2^(2/3))(-1)} + {3*(2^(1/3))*(-1)^(2)}+ (-1)^(3)]
=> (x-2)^3 = 2 - 6*(2^(2/3)) + 6*(2^(1/3))
=> (x-2)^3 = 2 - 6*[(2^(2/3))- (2^(1/3)]
=> (x-2)^3 = 2 - 6*(x-2)
=> (x-2)^3 = -6*x +14
=> (x-2)^3 + 6*x -14 =0
=> (x-2)^3 + 6*x -14 + 40 = 40
=> (x-2)^3 + 6x + 26 = 40
So, we get [(eqn1)] = 40
So, x^3 - 6x^2 +18x +18 =40..

So, Answer is
x^3 - 6x^2 +18x +18 =40..

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