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D( x )
x-2 = 0
x-2 = 0
x-2 = 0
x-2 = 0 // + 2
x = 2
x in (-oo:2) U (2:+oo)
(X^3+2*x^2-(9*x)+3)/(x-2) = 0
(X^3+2*x^2-9*x+3)/(x-2) = 0
X^3+2*x^2-9*x+3 = 0
DELTA = (-9)^2-(2*4*(X^3+3))
DELTA = 81-8*(X^3+3)
81-8*(X^3+3) = 0
81-8*(X^3+3) = 0
57-8*X^3 = 0
57-8*X^3 = 0
-8*X^3 = -57 // : -8
X^3 = 57/8
X^3 = 57/8 // ^ 1/3
X = (57/8)^(1/3)
DELTA = 0 <=> t_2 = (57/8)^(1/3)
x = 9/(2*2) i X = (57/8)^(1/3)
x = 9/4 i X = (57/8)^(1/3)
( x = ((81-8*(X^3+3))^(1/2)+9)/(2*2) or x = (9-(81-8*(X^3+3))^(1/2))/(2*2) ) i X > (57/8)^(1/3)
( x = ((81-8*(X^3+3))^(1/2)+9)/4 or x = (9-(81-8*(X^3+3))^(1/2))/4 ) i X > (57/8)^(1/3)
X-(57/8)^(1/3) > 0
X-(57/8)^(1/3) > 0 // + (57/8)^(1/3)
X > (57/8)^(1/3)
x in { 9/4, ((81-8*(X^3+3))^(1/2)+9)/4, (9-(81-8*(X^3+3))^(1/2))/4 }
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