1/x^4-x^2=0

Solution for 1/x^4-x^2=0 equation:

D( x )

x^4 = 0

x^4 = 0

x^4 = 0

1*x^4 = 0 // : 1

x^4 = 0

x = 0

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

1/(x^4)-x^2 = 0

x^-4-x^2 = 0

t_1 = x^2

1*t_1^-2-1*t_1^1 = 0

1*t_1^-2-1*t_1^1 = 0

(1*t_1^0-1*t_1^3)/(t_1^2) = 0 // * t_1^4

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

t_1^2

1-t_1^3 = 0

{ 1, -1 }

1

t_1 = 1

1-t_1^3 = 0

1

t_1-1

-t_1^2-t_1-1

1-t_1^3

t_1-1

t_1^3-t_1^2

1-t_1^2

t_1^2-t_1

1-t_1

t_1-1

0

-t_1^2-t_1-1 = 0

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

DELTA = -3

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 }