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D( x )
2*x-1 = 0
2*x-1 = 0
2*x-1 = 0
2*x-1 = 0 // + 1
2*x = 1 // : 2
x = 1/2
x in (-oo:1/2) U (1/2:+oo)
(6*x^3-(9*x^2)+13*x-5)/(2*x-1) = 0
(6*x^3-9*x^2+13*x-5)/(2*x-1) = 0
6*x^3-9*x^2+13*x-5 = 0
6*x^3-9*x^2+13*x-5 = 0
{ 1, -1, 5, -5 }
1
x = 1
6*x^3-9*x^2+13*x-5 = 5
1
-1
x = -1
6*x^3-9*x^2+13*x-5 = -33
-1
5
x = 5
6*x^3-9*x^2+13*x-5 = 585
5
-5
x = -5
6*x^3-9*x^2+13*x-5 = -1045
-5
{ 1/2, -1/2, 1/3, -1/3, 1/6, -1/6, -1/2, 1/2, -1/3, 1/3, -1/6, 1/6, 5/2, -5/2, 5/3, -5/3, 5/6, -5/6, -5/2, 5/2, -5/3, 5/3, -5/6, 5/6 }
1/2
x
1/2
6*x^3-9*x^2+13*x-5 = 0
1/2
x-1/2
6*x^2-6*x+10
6*x^3-9*x^2+13*x-5
x-1/2
3*x^2-6*x^3
13*x-6*x^2-5
6*x^2-3*x
10*x-5
5-10*x
0
6*x^2-6*x+10 = 0
DELTA = (-6)^2-(4*6*10)
DELTA = -204
DELTA < 0
x in { 1/2}
x-1/2 = 0
(x-1/2)/(2*x-1) = 0
x-1/2 = 0 // + 1/2
x = 1/2
x in { 1/2}
x belongs to the empty set
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