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

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Solution for 2-1/x-5/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)

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

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

t_1 = x^-1

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

2-5*t_1^2-t_1 = 0

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

DELTA = 41

DELTA > 0

t_1 = (41^(1/2)+1)/(-5*2) or t_1 = (1-41^(1/2))/(-5*2)

t_1 = (41^(1/2)+1)/(-10) or t_1 = (1-41^(1/2))/(-10)

t_1 = (41^(1/2)+1)/(-10)

x^-1-((41^(1/2)+1)/(-10)) = 0

1*x^-1 = (41^(1/2)+1)/(-10) // : 1

x^-1 = (41^(1/2)+1)/(-10)

-1 < 0

1/(x^1) = (41^(1/2)+1)/(-10) // * x^1

1 = ((41^(1/2)+1)/(-10))*x^1 // : (41^(1/2)+1)/(-10)

-10*(41^(1/2)+1)^-1 = x^1

x = -10*(41^(1/2)+1)^-1

t_1 = (1-41^(1/2))/(-10)

x^-1-((1-41^(1/2))/(-10)) = 0

1*x^-1 = (1-41^(1/2))/(-10) // : 1

x^-1 = (1-41^(1/2))/(-10)

-1 < 0

1/(x^1) = (1-41^(1/2))/(-10) // * x^1

1 = ((1-41^(1/2))/(-10))*x^1 // : (1-41^(1/2))/(-10)

-10*(1-41^(1/2))^-1 = x^1

x = -10*(1-41^(1/2))^-1

x in { -10*(41^(1/2)+1)^-1, -10*(1-41^(1/2))^-1 }

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