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

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

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

x^-1-x^-2+5 = 0

t_1 = x^-1

1*t_1^1-1*t_1^2+5 = 0

t_1-t_1^2+5 = 0

DELTA = 1^2-(-1*4*5)

DELTA = 21

DELTA > 0

t_1 = (21^(1/2)-1)/(-1*2) or t_1 = (-21^(1/2)-1)/(-1*2)

t_1 = (21^(1/2)-1)/(-2) or t_1 = (21^(1/2)+1)/2

t_1 = (21^(1/2)-1)/(-2)

x^-1-((21^(1/2)-1)/(-2)) = 0

1*x^-1 = (21^(1/2)-1)/(-2) // : 1

x^-1 = (21^(1/2)-1)/(-2)

-1 < 0

1/(x^1) = (21^(1/2)-1)/(-2) // * x^1

1 = ((21^(1/2)-1)/(-2))*x^1 // : (21^(1/2)-1)/(-2)

-2*(21^(1/2)-1)^-1 = x^1

x = -2*(21^(1/2)-1)^-1

t_1 = (21^(1/2)+1)/2

x^-1-((21^(1/2)+1)/2) = 0

1*x^-1 = (21^(1/2)+1)/2 // : 1

x^-1 = (21^(1/2)+1)/2

-1 < 0

1/(x^1) = (21^(1/2)+1)/2 // * x^1

1 = ((21^(1/2)+1)/2)*x^1 // : (21^(1/2)+1)/2

2*(21^(1/2)+1)^-1 = x^1

x = 2*(21^(1/2)+1)^-1

x in { -2*(21^(1/2)-1)^-1, 2*(21^(1/2)+1)^-1 }

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