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

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Solution for 4-1/x-2/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)

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

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

t_1 = x^-1

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

4-2*t_1^2-t_1 = 0

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

DELTA = 33

DELTA > 0

t_1 = (33^(1/2)+1)/(-2*2) or t_1 = (1-33^(1/2))/(-2*2)

t_1 = (33^(1/2)+1)/(-4) or t_1 = (1-33^(1/2))/(-4)

t_1 = (33^(1/2)+1)/(-4)

x^-1-((33^(1/2)+1)/(-4)) = 0

1*x^-1 = (33^(1/2)+1)/(-4) // : 1

x^-1 = (33^(1/2)+1)/(-4)

-1 < 0

1/(x^1) = (33^(1/2)+1)/(-4) // * x^1

1 = ((33^(1/2)+1)/(-4))*x^1 // : (33^(1/2)+1)/(-4)

-4*(33^(1/2)+1)^-1 = x^1

x = -4*(33^(1/2)+1)^-1

t_1 = (1-33^(1/2))/(-4)

x^-1-((1-33^(1/2))/(-4)) = 0

1*x^-1 = (1-33^(1/2))/(-4) // : 1

x^-1 = (1-33^(1/2))/(-4)

-1 < 0

1/(x^1) = (1-33^(1/2))/(-4) // * x^1

1 = ((1-33^(1/2))/(-4))*x^1 // : (1-33^(1/2))/(-4)

-4*(1-33^(1/2))^-1 = x^1

x = -4*(1-33^(1/2))^-1

x in { -4*(33^(1/2)+1)^-1, -4*(1-33^(1/2))^-1 }

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