5-1/x-8/x^2=0

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Solution for 5-1/x-8/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)

5-(1/x)-(8/(x^2)) = 0

5-x^-1-8*x^-2 = 0

t_1 = x^-1

5-8*t_1^2-1*t_1^1 = 0

5-8*t_1^2-t_1 = 0

DELTA = (-1)^2-(-8*4*5)

DELTA = 161

DELTA > 0

t_1 = (161^(1/2)+1)/(-8*2) or t_1 = (1-161^(1/2))/(-8*2)

t_1 = (161^(1/2)+1)/(-16) or t_1 = (1-161^(1/2))/(-16)

t_1 = (161^(1/2)+1)/(-16)

x^-1-((161^(1/2)+1)/(-16)) = 0

1*x^-1 = (161^(1/2)+1)/(-16) // : 1

x^-1 = (161^(1/2)+1)/(-16)

-1 < 0

1/(x^1) = (161^(1/2)+1)/(-16) // * x^1

1 = ((161^(1/2)+1)/(-16))*x^1 // : (161^(1/2)+1)/(-16)

-16*(161^(1/2)+1)^-1 = x^1

x = -16*(161^(1/2)+1)^-1

t_1 = (1-161^(1/2))/(-16)

x^-1-((1-161^(1/2))/(-16)) = 0

1*x^-1 = (1-161^(1/2))/(-16) // : 1

x^-1 = (1-161^(1/2))/(-16)

-1 < 0

1/(x^1) = (1-161^(1/2))/(-16) // * x^1

1 = ((1-161^(1/2))/(-16))*x^1 // : (1-161^(1/2))/(-16)

-16*(1-161^(1/2))^-1 = x^1

x = -16*(1-161^(1/2))^-1

x in { -16*(161^(1/2)+1)^-1, -16*(1-161^(1/2))^-1 }

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