(X^3-4x)/x^2+4=0

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Solution for (X^3-4x)/x^2+4=0 equation: 


D( x )

x^2 = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

x in (-oo:0) U (0:+oo)

(X^3-(4*x))/(x^2)+4 = 0

(X^3-4*x)/(x^2)+4 = 0

(X^3-4*x)/(x^2)+(4*x^2)/(x^2) = 0

X^3+4*x^2-4*x = 0

(X^3+4*x^2-4*x)/(x^2) = 0

(X^3+4*x^2-4*x)/(x^2) = 0 // * x^2

X^3+4*x^2-4*x = 0

X^3+4*x^2-4*x = 0

DELTA = (-4)^2-(4*4*X^3)

DELTA = 16-16*X^3

16-16*X^3 = 0

-16*X^3 = -16 // : -16

X^3 = 1

X^3 = 1 // ^ 1/3

X = 1

DELTA = 0  <=>  t_3 = 1

x = 4/(2*4) i X = 1

x = 1/2 i X = 1

( x = ((16-16*X^3)^(1/2)+4)/(2*4) or x = (4-(16-16*X^3)^(1/2))/(2*4) ) i X > 1

( x = ((16-16*X^3)^(1/2)+4)/8 or x = (4-(16-16*X^3)^(1/2))/8 ) i X > 1

X-1 > 0

X-1 > 0 // + 1

X > 1

x in { 1/2, ((16-16*X^3)^(1/2)+4)/8, (4-(16-16*X^3)^(1/2))/8 }

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