3x^4+12/x^2-15

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Solution for 3x^4+12/x^2-15 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)

3*x^4+12/(x^2)-15 = 0

3*x^4+12*x^-2-15 = 0

t_1 = x^2

3*t_1^2+12*t_1^-1-15*t_1^0 = 0

(3*t_1^3-15*t_1^1+12*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(3*t_1^3-15*t_1^1+12*t_1^0) = 0

t_1^1

3*t_1^3-15*t_1+12 = 0

{ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 12, -12 }

1

t_1 = 1

3*t_1^3-15*t_1+12 = 0

1

t_1-1

3*t_1^2+3*t_1-12

3*t_1^3-15*t_1+12

t_1-1

3*t_1^2-3*t_1^3

3*t_1^2-15*t_1+12

3*t_1-3*t_1^2

12-12*t_1

12*t_1-12

0

3*t_1^2+3*t_1-12 = 0

DELTA = 3^2-(-12*3*4)

DELTA = 153

DELTA > 0

t_1 = (153^(1/2)-3)/(2*3) or t_1 = (-153^(1/2)-3)/(2*3)

t_1 = (3*17^(1/2)-3)/6 or t_1 = (-3*17^(1/2)-3)/6

t_1 in { (-3*17^(1/2)-3)/6, (3*17^(1/2)-3)/6, 1} 

t_1 = (-3*17^(1/2)-3)/6

x^2-((-3*17^(1/2)-3)/6) = 0

1*x^2 = (-3*17^(1/2)-3)/6 // : 1

x^2 = (-3*17^(1/2)-3)/6

t_1 = (3*17^(1/2)-3)/6

x^2-((3*17^(1/2)-3)/6) = 0

1*x^2 = (3*17^(1/2)-3)/6 // : 1

x^2 = (3*17^(1/2)-3)/6

x^2 = (3*17^(1/2)-3)/6 // ^ 1/2

abs(x) = ((3*17^(1/2)-3)^(1/2))/(6^(1/2))

x = ((3*17^(1/2)-3)^(1/2))/(6^(1/2)) or x = -(((3*17^(1/2)-3)^(1/2))/(6^(1/2)))

t_1 = 1

x^2-1 = 0

1*x^2 = 1 // : 1

x^2 = 1

x^2 = 1 // ^ 1/2

abs(x) = 1

x = 1 or x = -1

x in { ((3*17^(1/2)-3)^(1/2))/(6^(1/2)), -(((3*17^(1/2)-3)^(1/2))/(6^(1/2))), 1, -1 }

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