(z2-25/z)/(z-5/z-8)

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Solution for (z2-25/z)/(z-5/z-8) equation: 


D( z )

z-(5/z)-8 = 0

z = 0

z-(5/z)-8 = 0

z-(5/z)-8 = 0

z-5*z^-1-8 = 0

1*z^1-5*z^-1-8*z^0 = 0

(1*z^2-8*z^1-5*z^0)/(z^1) = 0 // * z^2

z^1*(1*z^2-8*z^1-5*z^0) = 0

z^1

z^2-8*z-5 = 0

z^2-8*z-5 = 0

DELTA = (-8)^2-(-5*1*4)

DELTA = 84

DELTA > 0

z = (84^(1/2)+8)/(1*2) or z = (8-84^(1/2))/(1*2)

z = (2*21^(1/2)+8)/2 or z = (8-2*21^(1/2))/2

z in { (8-2*21^(1/2))/2, (2*21^(1/2)+8)/2} 

z = 0

z = 0

z in (-oo:(8-2*21^(1/2))/2) U ((8-2*21^(1/2))/2:0) U (0:(2*21^(1/2)+8)/2) U ((2*21^(1/2)+8)/2:+oo)

(z^2-(25/z))/(z-(5/z)-8) = 0

(z^2-25*z^-1)/(z-5*z^-1-8) = 0

z^2-25*z^-1 = 0

z^-1*(z^3-25) = 0

1*z^3 = 25 // : 1

z^3 = 25

z^3 = 25 // ^ 1/3

z = 25^(1/3)

z^-1*(z-25^(1/3)) = 0

z-5*z^-1-8 = 0

1*z^1-5*z^-1-8*z^0 = 0

(1*z^2-8*z^1-5*z^0)/(z^1) = 0 // * z^2

z^1*(1*z^2-8*z^1-5*z^0) = 0

z^1

z^2-8*z-5 = 0

z^2-8*z-5 = 0

DELTA = (-8)^2-(-5*1*4)

DELTA = 84

DELTA > 0

z = (84^(1/2)+8)/(1*2) or z = (8-84^(1/2))/(1*2)

z = (2*21^(1/2)+8)/2 or z = (8-2*21^(1/2))/2

z in { (8-2*21^(1/2))/2, (2*21^(1/2)+8)/2} 

(z-((8-2*21^(1/2))/2))*(z-((2*21^(1/2)+8)/2)) = 0

(z^-1*(z-25^(1/3)))/((z-((8-2*21^(1/2))/2))*(z-((2*21^(1/2)+8)/2))) = 0

( z-25^(1/3) )

z-25^(1/3) = 0 // + 25^(1/3)

z = 25^(1/3)

( z^-1 )

1*z^-1 = 0 // : 1

z^-1 = 0

z należy do O

z = 25^(1/3)

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