1/x^2-1/x-2=0

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


D( x )

x = 0

x^2 = 0

x = 0

x = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

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

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

x^-2-x^-1-2 = 0

t_1 = x^-1

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

t_1^2-t_1-2 = 0

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

DELTA = 9

DELTA > 0

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

t_1 = 2 or t_1 = -1

t_1 = -1

x^-1+1 = 0

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

x^-1 = -1

-1 < 0

1/(x^1) = -1 // * x^1

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

-1 = x^1

x = -1

t_1 = 2

x^-1-2 = 0

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

x^-1 = 2

-1 < 0

1/(x^1) = 2 // * x^1

1 = 2*x^1 // : 2

1/2 = x^1

x = 1/2

x in { -1, 1/2 }

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