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

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

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

t_1 = x^-1

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

4-t_1^2-t_1 = 0

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

DELTA = 17

DELTA > 0

t_1 = (17^(1/2)+1)/(-1*2) or t_1 = (1-17^(1/2))/(-1*2)

t_1 = (17^(1/2)+1)/(-2) or t_1 = (1-17^(1/2))/(-2)

t_1 = (17^(1/2)+1)/(-2)

x^-1-((17^(1/2)+1)/(-2)) = 0

1*x^-1 = (17^(1/2)+1)/(-2) // : 1

x^-1 = (17^(1/2)+1)/(-2)

-1 < 0

1/(x^1) = (17^(1/2)+1)/(-2) // * x^1

1 = ((17^(1/2)+1)/(-2))*x^1 // : (17^(1/2)+1)/(-2)

-2*(17^(1/2)+1)^-1 = x^1

x = -2*(17^(1/2)+1)^-1

t_1 = (1-17^(1/2))/(-2)

x^-1-((1-17^(1/2))/(-2)) = 0

1*x^-1 = (1-17^(1/2))/(-2) // : 1

x^-1 = (1-17^(1/2))/(-2)

-1 < 0

1/(x^1) = (1-17^(1/2))/(-2) // * x^1

1 = ((1-17^(1/2))/(-2))*x^1 // : (1-17^(1/2))/(-2)

-2*(1-17^(1/2))^-1 = x^1

x = -2*(1-17^(1/2))^-1

x in { -2*(17^(1/2)+1)^-1, -2*(1-17^(1/2))^-1 }

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