x^4+3x^2-6/x^2+2

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Solution for x^4+3x^2-6/x^2+2 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^4+3*x^2-(6/(x^2))+2 = 0

x^4+3*x^2-6*x^-2+2 = 0

t_1 = x^2

1*t_1^2+3*t_1^1-6*t_1^-1+2 = 0

1*t_1^2+3*t_1^1-6*t_1^-1+2*t_1^0 = 0

(1*t_1^3+3*t_1^2+2*t_1^1-6*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(1*t_1^3+3*t_1^2+2*t_1^1-6*t_1^0) = 0

t_1^1

t_1^3+3*t_1^2+2*t_1-6 = 0

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

1

t_1 = 1

t_1^3+3*t_1^2+2*t_1-6 = 0

1

t_1-1

t_1^2+4*t_1+6

t_1^3+3*t_1^2+2*t_1-6

t_1-1

t_1^2-t_1^3

4*t_1^2+2*t_1-6

4*t_1-4*t_1^2

6*t_1-6

6-6*t_1

0

t_1^2+4*t_1+6 = 0

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

DELTA = -8

DELTA < 0

t_1 in { 1} 

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 { 1, -1 }

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