4+1/x=1/x^2

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Solution for 4+1/x=1/x^2 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)

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

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

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

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

t_1 = x^-1

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

t_1-t_1^2+4 = 0

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

DELTA = 17

DELTA > 0

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

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

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

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