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D( x )
x = 0
x = 0
x = 0
x in (-oo:0) U (0:+oo)
(5*x-4)*(5*x-4) = 1/x // - 1/x
(5*x-4)*(5*x-4)-(1/x) = 0
(5*x-4)*(5*x-4)-x^-1 = 0
(5*x-4)^2-1/x = 0
(x*(5*x-4)^2)/x-1/x = 0
x*(5*x-4)^2-1 = 0
25*x^3-40*x^2+16*x-1 = 0
25*x^3-40*x^2+16*x-1 = 0
25*x^3-40*x^2+16*x-1 = 0
{ 1, -1 }
1
x = 1
25*x^3-40*x^2+16*x-1 = 0
1
x-1
25*x^2-15*x+1
25*x^3-40*x^2+16*x-1
x-1
25*x^2-25*x^3
16*x-15*x^2-1
15*x^2-15*x
x-1
1-x
0
25*x^2-15*x+1 = 0
DELTA = (-15)^2-(1*4*25)
DELTA = 125
DELTA > 0
x = (125^(1/2)+15)/(2*25) or x = (15-125^(1/2))/(2*25)
x = (5*5^(1/2)+15)/50 or x = (15-5*5^(1/2))/50
x in { (15-5*5^(1/2))/50, (5*5^(1/2)+15)/50, 1}
(x-((15-5*5^(1/2))/50))*(x-((5*5^(1/2)+15)/50))*(x-1) = 0
((x-((15-5*5^(1/2))/50))*(x-((5*5^(1/2)+15)/50))*(x-1))/x = 0
((x-((15-5*5^(1/2))/50))*(x-((5*5^(1/2)+15)/50))*(x-1))/x = 0 // * x
(x-((15-5*5^(1/2))/50))*(x-((5*5^(1/2)+15)/50))*(x-1) = 0
( x-((15-5*5^(1/2))/50) )
x-((15-5*5^(1/2))/50) = 0 // + (15-5*5^(1/2))/50
x = (15-5*5^(1/2))/50
( x-((5*5^(1/2)+15)/50) )
x-((5*5^(1/2)+15)/50) = 0 // + (5*5^(1/2)+15)/50
x = (5*5^(1/2)+15)/50
( x-1 )
x-1 = 0 // + 1
x = 1
x in { (15-5*5^(1/2))/50, (5*5^(1/2)+15)/50, 1 }
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