(x^3-4x^2+x)/(x-2)

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Solution for (x^3-4x^2+x)/(x-2) equation: 


D( x )

x-2 = 0

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

x in (-oo:2) U (2:+oo)

(x^3-(4*x^2)+x)/(x-2) = 0

(x^3-4*x^2+x)/(x-2) = 0

x^3-4*x^2+x = 0

x*(x^2-4*x+1) = 0

x^2-4*x+1 = 0

DELTA = (-4)^2-(1*1*4)

DELTA = 12

DELTA > 0

x = (12^(1/2)+4)/(1*2) or x = (4-12^(1/2))/(1*2)

x = (2*3^(1/2)+4)/2 or x = (4-2*3^(1/2))/2

x*(x-((4-2*3^(1/2))/2))*(x-((2*3^(1/2)+4)/2)) = 0

(x*(x-((4-2*3^(1/2))/2))*(x-((2*3^(1/2)+4)/2)))/(x-2) = 0

( x-((2*3^(1/2)+4)/2) )

x-((2*3^(1/2)+4)/2) = 0 // + (2*3^(1/2)+4)/2

x = (2*3^(1/2)+4)/2

( x-((4-2*3^(1/2))/2) )

x-((4-2*3^(1/2))/2) = 0 // + (4-2*3^(1/2))/2

x = (4-2*3^(1/2))/2

( x )

x = 0

x in { (2*3^(1/2)+4)/2, (4-2*3^(1/2))/2, 0 }

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