(x3-4x2+4x-1)/(x-1)

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Solution for (x3-4x2+4x-1)/(x-1) equation: 


D( x )

x-1 = 0

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

x in (-oo:1) U (1:+oo)

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

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

x^3-4*x^2+4*x-1 = 0

x^3-4*x^2+4*x-1 = 0

{ 1, -1 }

1

x = 1

x^3-4*x^2+4*x-1 = 0

1

x-1

x^2-3*x+1

x^3-4*x^2+4*x-1

x-1

x^2-x^3

4*x-3*x^2-1

3*x^2-3*x

x-1

1-x

0

x^2-3*x+1 = 0

DELTA = (-3)^2-(1*1*4)

DELTA = 5

DELTA > 0

x = (5^(1/2)+3)/(1*2) or x = (3-5^(1/2))/(1*2)

x = (5^(1/2)+3)/2 or x = (3-5^(1/2))/2

x in { (3-5^(1/2))/2, (5^(1/2)+3)/2, 1} 

(x-((3-5^(1/2))/2))*(x-((5^(1/2)+3)/2))*(x-1) = 0

(x-((3-5^(1/2))/2))*(x-((5^(1/2)+3)/2)) = 0

( x-((3-5^(1/2))/2) )

x-((3-5^(1/2))/2) = 0 // + (3-5^(1/2))/2

x = (3-5^(1/2))/2

( x-((5^(1/2)+3)/2) )

x-((5^(1/2)+3)/2) = 0 // + (5^(1/2)+3)/2

x = (5^(1/2)+3)/2

x in { (3-5^(1/2))/2, (5^(1/2)+3)/2 }

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