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

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Solution for (1/x)+(1/x^2)-(1/x^3) equation: 


D( x )

x^3 = 0

x = 0

x^2 = 0

x^3 = 0

x^3 = 0

1*x^3 = 0 // : 1

x^3 = 0

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

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

x^-1+x^-2-x^-3 = 0

t_1 = x^-1

1*t_1^2-1*t_1^3+1*t_1^1 = 0

t_1^2-t_1^3+t_1 = 0

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

t_1-t_1^2+1 = 0

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

DELTA = 5

DELTA > 0

t_1 = (5^(1/2)-1)/(-1*2) or t_1 = (-5^(1/2)-1)/(-1*2)

t_1 = (5^(1/2)-1)/(-2) or t_1 = (5^(1/2)+1)/2

t_1 = 0

t_1 = 0

t_1 = (5^(1/2)-1)/(-2)

x^-1-((5^(1/2)-1)/(-2)) = 0

1*x^-1 = (5^(1/2)-1)/(-2) // : 1

x^-1 = (5^(1/2)-1)/(-2)

-1 < 0

1/(x^1) = (5^(1/2)-1)/(-2) // * x^1

1 = ((5^(1/2)-1)/(-2))*x^1 // : (5^(1/2)-1)/(-2)

-2*(5^(1/2)-1)^-1 = x^1

x = -2*(5^(1/2)-1)^-1

t_1 = (5^(1/2)+1)/2

x^-1-((5^(1/2)+1)/2) = 0

1*x^-1 = (5^(1/2)+1)/2 // : 1

x^-1 = (5^(1/2)+1)/2

-1 < 0

1/(x^1) = (5^(1/2)+1)/2 // * x^1

1 = ((5^(1/2)+1)/2)*x^1 // : (5^(1/2)+1)/2

2*(5^(1/2)+1)^-1 = x^1

x = 2*(5^(1/2)+1)^-1

t_1 = 0

x^-1+0 = 0

x^-1 = 0

1*x^-1 = 0 // : 1

x^-1 = 0

x naleu017Cy do O

x in { -2*(5^(1/2)-1)^-1, 2*(5^(1/2)+1)^-1 }

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