(3/X^2)+8X^2-12

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Solution for (3/X^2)+8X^2-12 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)

8*X^2+3/(X^2)-12 = 0

8*X^2+3*X^-2-12 = 0

t_1 = X^2

8*t_1^1+3*t_1^-1-12 = 0

8*t_1^1+3*t_1^-1-12*t_1^0 = 0

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

t_1^1*(8*t_1^2-12*t_1^1+3*t_1^0) = 0

t_1^1

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

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

DELTA = (-12)^2-(3*4*8)

DELTA = 48

DELTA > 0

t_1 = (48^(1/2)+12)/(2*8) or t_1 = (12-48^(1/2))/(2*8)

t_1 = (4*3^(1/2)+12)/16 or t_1 = (12-4*3^(1/2))/16

t_1 in { (12-4*3^(1/2))/16, (4*3^(1/2)+12)/16} 

t_1 = (12-4*3^(1/2))/16

X^2-((12-4*3^(1/2))/16) = 0

1*X^2 = (12-4*3^(1/2))/16 // : 1

X^2 = (12-4*3^(1/2))/16

X^2 = (12-4*3^(1/2))/16 // ^ 1/2

abs(X) = ((12-4*3^(1/2))^(1/2))/4

X = ((12-4*3^(1/2))^(1/2))/4 or X = -(((12-4*3^(1/2))^(1/2))/4)

t_1 = (4*3^(1/2)+12)/16

X^2-((4*3^(1/2)+12)/16) = 0

1*X^2 = (4*3^(1/2)+12)/16 // : 1

X^2 = (4*3^(1/2)+12)/16

X^2 = (4*3^(1/2)+12)/16 // ^ 1/2

abs(X) = ((4*3^(1/2)+12)^(1/2))/4

X = ((4*3^(1/2)+12)^(1/2))/4 or X = -(((4*3^(1/2)+12)^(1/2))/4)

X in { ((12-4*3^(1/2))^(1/2))/4, -(((12-4*3^(1/2))^(1/2))/4), ((4*3^(1/2)+12)^(1/2))/4, -(((4*3^(1/2)+12)^(1/2))/4) }

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