9x^2-1/x^2-1

Solution for 9x^2-1/x^2-1 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)

9*x^2-(1/(x^2))-1 = 0

9*x^2-x^-2-1 = 0

t_1 = x^2

9*t_1^1-1*t_1^-1-1 = 0

9*t_1^1-1*t_1^-1-1*t_1^0 = 0

(9*t_1^2-1*t_1^1-1*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(9*t_1^2-1*t_1^1-1*t_1^0) = 0

t_1^1

9*t_1^2-t_1-1 = 0

9*t_1^2-t_1-1 = 0

DELTA = (-1)^2-(-1*4*9)

DELTA = 37

DELTA > 0

t_1 = (37^(1/2)+1)/(2*9) or t_1 = (1-37^(1/2))/(2*9)

t_1 = (37^(1/2)+1)/18 or t_1 = (1-37^(1/2))/18

t_1 in { (1-37^(1/2))/18, (37^(1/2)+1)/18} 

t_1 = (1-37^(1/2))/18

x^2-((1-37^(1/2))/18) = 0

1*x^2 = (1-37^(1/2))/18 // : 1

x^2 = (1-37^(1/2))/18

t_1 = (37^(1/2)+1)/18

x^2-((37^(1/2)+1)/18) = 0

1*x^2 = (37^(1/2)+1)/18 // : 1

x^2 = (37^(1/2)+1)/18

x^2 = (37^(1/2)+1)/18 // ^ 1/2

abs(x) = ((37^(1/2)+1)^(1/2))/(3*2^(1/2))

x = ((37^(1/2)+1)^(1/2))/(3*2^(1/2)) or x = -(((37^(1/2)+1)^(1/2))/(3*2^(1/2)))

x in { ((37^(1/2)+1)^(1/2))/(3*2^(1/2)), -(((37^(1/2)+1)^(1/2))/(3*2^(1/2))) }