3x-1/x-24

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Solution for 3x-1/x-24 equation:


D( x )

x = 0

x = 0

x = 0

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

3*x-(1/x)-2 < 4 // - 4

3*x-(1/x)-4-2 < 0

3*x-x^-1-4-2 < 0

3*x-x^-1-4-2 = 0

3*x^1-1*x^-1-6*x^0 = 0

(3*x^2-6*x^1-1*x^0)/(x^1) = 0 // * x^2

x^1*(3*x^2-6*x^1-1*x^0) = 0

x^1

3*x^2-6*x-1 = 0

3*x^2-6*x-1 = 0

DELTA = (-6)^2-(-1*3*4)

DELTA = 48

DELTA > 0

x = (48^(1/2)+6)/(2*3) or x = (6-48^(1/2))/(2*3)

x = (4*3^(1/2)+6)/6 or x = (6-4*3^(1/2))/6

x in { (6-4*3^(1/2))/6, (4*3^(1/2)+6)/6}

(x-((6-4*3^(1/2))/6))*(x-((4*3^(1/2)+6)/6)) < 0

(-oo:(6-4*3^(1/2))/6) ((6-4*3^(1/2))/6:(4*3^(1/2)+6)/6) ((4*3^(1/2)+6)/6:+oo) x-((6-4*3^(1/2))/6) - + + x-((4*3^(1/2)+6)/6) - - +

x in ((6-4*3^(1/2))/6:0) U (0:(4*3^(1/2)+6)/6)

((6-4*3^(1/2))/6:0) U (0:(4*3^(1/2)+6)/6)

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