x^4-1/x^2

Solution for x^4-1/x^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-(1/(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_1^3-1*t_1^0)/(t_1^1) = 0 // * t_1^2

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

t_1^1

t_1^3-1 = 0

{ 1, -1 }

1

t_1 = 1

t_1^3-1 = 0

1

t_1-1

t_1^2+t_1+1

t_1^3-1

t_1-1

t_1^2-t_1^3

t_1^2-1

t_1-t_1^2

t_1-1

1-t_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 }