x^2-1=6/x^2

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Solution for x^2-1=6/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^2-1 = 6/(x^2) // - 6/(x^2)

x^2-(6/(x^2))-1 = 0

x^2-6*x^-2-1 = 0

t_1 = x^2

1*t_1^1-6*t_1^-1-1 = 0

1*t_1^1-6*t_1^-1-1*t_1^0 = 0

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

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

t_1^1

t_1^2-t_1-6 = 0

t_1^2-t_1-6 = 0

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

DELTA = 25

DELTA > 0

t_1 = (25^(1/2)+1)/(1*2) or t_1 = (1-25^(1/2))/(1*2)

t_1 = 3 or t_1 = -2

t_1 in { -2, 3} 

t_1 = -2

x^2+2 = 0

1*x^2 = -2 // : 1

x^2 = -2

t_1 = 3

x^2-3 = 0

1*x^2 = 3 // : 1

x^2 = 3

x^2 = 3 // ^ 1/2

abs(x) = 3^(1/2)

x = 3^(1/2) or x = -3^(1/2)

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

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