x^-2-x^-1=4/3

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Solution for x^-2-x^-1=4/3 equation: 


D( x )

x = 0

x = 0

x = 0

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

x^-2-x^-1 = 4/3 // - 4/3

x^-2-x^-1-(4/3) = 0

x^-2-x^-1-4/3 = 0

t_1 = x^-1

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

t_1^2-t_1-4/3 = 0

DELTA = (-1)^2-(-4/3*1*4)

DELTA = 19/3

DELTA > 0

t_1 = ((19/3)^(1/2)+1)/(1*2) or t_1 = (1-(19/3)^(1/2))/(1*2)

t_1 = ((19/3)^(1/2)+1)/2 or t_1 = (1-(19/3)^(1/2))/2

t_1 = (1-(19/3)^(1/2))/2

x^-1-((1-(19/3)^(1/2))/2) = 0

1*x^-1 = (1-(19/3)^(1/2))/2 // : 1

x^-1 = (1-(19/3)^(1/2))/2

-1 < 0

1/(x^1) = (1-(19/3)^(1/2))/2 // * x^1

1 = ((1-(19/3)^(1/2))/2)*x^1 // : (1-(19/3)^(1/2))/2

2*(1-(19/3)^(1/2))^-1 = x^1

x = 2*(1-(19/3)^(1/2))^-1

t_1 = ((19/3)^(1/2)+1)/2

x^-1-(((19/3)^(1/2)+1)/2) = 0

1*x^-1 = ((19/3)^(1/2)+1)/2 // : 1

x^-1 = ((19/3)^(1/2)+1)/2

-1 < 0

1/(x^1) = ((19/3)^(1/2)+1)/2 // * x^1

1 = (((19/3)^(1/2)+1)/2)*x^1 // : ((19/3)^(1/2)+1)/2

2*((19/3)^(1/2)+1)^-1 = x^1

x = 2*((19/3)^(1/2)+1)^-1

x in { 2*(1-(19/3)^(1/2))^-1, 2*((19/3)^(1/2)+1)^-1 }

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