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D( x )
5*x-2 = 0
5*x-2 = 0
5*x-2 = 0
5*x-2 = 0 // + 2
5*x = 2 // : 5
x = 2/5
x in (-oo:2/5) U (2/5:+oo)
(x^3-(12*x)-9)/(5*x-2) = 0
(x^3-12*x-9)/(5*x-2) = 0
x^3-12*x-9 = 0
x^3-12*x-9 = 0
{ 1, -1, 3, -3, 9, -9 }
1
x = 1
x^3-12*x-9 = -20
1
-1
x = -1
x^3-12*x-9 = 2
-1
3
x = 3
x^3-12*x-9 = -18
3
-3
x = -3
x^3-12*x-9 = 0
-3
x+3
x^2-3*x-3
x^3-12*x-9
x+3
-x^3-3*x^2
-3*x^2-12*x-9
3*x^2+9*x
-3*x-9
3*x+9
0
x^2-3*x-3 = 0
DELTA = (-3)^2-(-3*1*4)
DELTA = 21
DELTA > 0
x = (21^(1/2)+3)/(1*2) or x = (3-21^(1/2))/(1*2)
x = (21^(1/2)+3)/2 or x = (3-21^(1/2))/2
x in { (3-21^(1/2))/2, (21^(1/2)+3)/2, -3}
(x-((3-21^(1/2))/2))*(x-((21^(1/2)+3)/2))*(x+3) = 0
((x-((3-21^(1/2))/2))*(x-((21^(1/2)+3)/2))*(x+3))/(5*x-2) = 0
( x+3 )
x+3 = 0 // - 3
x = -3
( x-((21^(1/2)+3)/2) )
x-((21^(1/2)+3)/2) = 0 // + (21^(1/2)+3)/2
x = (21^(1/2)+3)/2
( x-((3-21^(1/2))/2) )
x-((3-21^(1/2))/2) = 0 // + (3-21^(1/2))/2
x = (3-21^(1/2))/2
x in { -3, (21^(1/2)+3)/2, (3-21^(1/2))/2 }
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