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D( x )
3*x+1 = 0
3*x+1 = 0
3*x+1 = 0
3*x+1 = 0 // - 1
3*x = -1 // : 3
x = -1/3
x in (-oo:-1/3) U (-1/3:+oo)
(27*x^3-(9*x^2)+2)/(3*x+1) = 0
(27*x^3-9*x^2+2)/(3*x+1) = 0
27*x^3-9*x^2+2 = 0
27*x^3-9*x^2+2 = 0
{ 1, -1, 2, -2 }
1
x = 1
27*x^3-9*x^2+2 = 20
1
-1
x = -1
27*x^3-9*x^2+2 = -34
-1
2
x = 2
27*x^3-9*x^2+2 = 182
2
-2
x = -2
27*x^3-9*x^2+2 = -250
-2
{ 1/3, -1/3, 1/9, -1/9, 1/27, -1/27, -1/3, 1/3, -1/9, 1/9, -1/27, 1/27, 2/3, -2/3, 2/9, -2/9, 2/27, -2/27, -2/3, 2/3, -2/9, 2/9, -2/27, 2/27 }
1/3
x
1/3
27*x^3-9*x^2+2 = 2
1/3
-1/3
x
-1/3
27*x^3-9*x^2+2 = 0
-1/3
x+1/3
27*x^2-18*x+6
27*x^3-9*x^2+2
x+1/3
-27*x^3-9*x^2
2-18*x^2
18*x^2+6*x
6*x+2
-6*x-2
0
27*x^2-18*x+6 = 0
DELTA = (-18)^2-(4*6*27)
DELTA = -324
DELTA < 0
x in { -1/3}
x+1/3 = 0
(x+1/3)/(3*x+1) = 0
x+1/3 = 0 // - 1/3
x = -1/3
x in { -1/3}
x belongs to the empty set
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