4-1/x-9/x^2=0

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Solution for 4-1/x-9/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)-(9/(x^2)) = 0

4-x^-1-9*x^-2 = 0

t_1 = x^-1

4-9*t_1^2-1*t_1^1 = 0

4-9*t_1^2-t_1 = 0

DELTA = (-1)^2-(-9*4*4)

DELTA = 145

DELTA > 0

t_1 = (145^(1/2)+1)/(-9*2) or t_1 = (1-145^(1/2))/(-9*2)

t_1 = (145^(1/2)+1)/(-18) or t_1 = (1-145^(1/2))/(-18)

t_1 = (145^(1/2)+1)/(-18)

x^-1-((145^(1/2)+1)/(-18)) = 0

1*x^-1 = (145^(1/2)+1)/(-18) // : 1

x^-1 = (145^(1/2)+1)/(-18)

-1 < 0

1/(x^1) = (145^(1/2)+1)/(-18) // * x^1

1 = ((145^(1/2)+1)/(-18))*x^1 // : (145^(1/2)+1)/(-18)

-18*(145^(1/2)+1)^-1 = x^1

x = -18*(145^(1/2)+1)^-1

t_1 = (1-145^(1/2))/(-18)

x^-1-((1-145^(1/2))/(-18)) = 0

1*x^-1 = (1-145^(1/2))/(-18) // : 1

x^-1 = (1-145^(1/2))/(-18)

-1 < 0

1/(x^1) = (1-145^(1/2))/(-18) // * x^1

1 = ((1-145^(1/2))/(-18))*x^1 // : (1-145^(1/2))/(-18)

-18*(1-145^(1/2))^-1 = x^1

x = -18*(1-145^(1/2))^-1

x in { -18*(145^(1/2)+1)^-1, -18*(1-145^(1/2))^-1 }

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