(z^3-10z+3)/(z-3)

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Solution for (z^3-10z+3)/(z-3) equation: 


D( z )

z-3 = 0

z-3 = 0

z-3 = 0

z-3 = 0 // + 3

z = 3

z in (-oo:3) U (3:+oo)

(z^3-(10*z)+3)/(z-3) = 0

(z^3-10*z+3)/(z-3) = 0

z^3-10*z+3 = 0

z^3-10*z+3 = 0

{ 1, -1, 3, -3 }

1

z = 1

z^3-10*z+3 = -6

1

-1

z = -1

z^3-10*z+3 = 12

-1

3

z = 3

z^3-10*z+3 = 0

3

z-3

z^2+3*z-1

z^3-10*z+3

z-3

3*z^2-z^3

3*z^2-10*z+3

9*z-3*z^2

3-z

z-3

0

z^2+3*z-1 = 0

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

DELTA = 13

DELTA > 0

z = (13^(1/2)-3)/(1*2) or z = (-13^(1/2)-3)/(1*2)

z = (13^(1/2)-3)/2 or z = (-(13^(1/2)+3))/2

z in { (-(13^(1/2)+3))/2, (13^(1/2)-3)/2, 3} 

(z+(13^(1/2)+3)/2)*(z-((13^(1/2)-3)/2))*(z-3) = 0

(z+(13^(1/2)+3)/2)*(z-((13^(1/2)-3)/2)) = 0

( z+(13^(1/2)+3)/2 )

z+(13^(1/2)+3)/2 = 0 // - (13^(1/2)+3)/2

z = -((13^(1/2)+3)/2)

( z-((13^(1/2)-3)/2) )

z-((13^(1/2)-3)/2) = 0 // + (13^(1/2)-3)/2

z = (13^(1/2)-3)/2

z in { -((13^(1/2)+3)/2), (13^(1/2)-3)/2 }

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