1/x^2-3=8/x

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Solution for 1/x^2-3=8/x 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^2)-3 = 8/x // - 8/x

1/(x^2)-(8/x)-3 = 0

1/(x^2)-8*x^-1-3 = 0

x^-2-8*x^-1-3 = 0

t_1 = x^-1

1*t_1^2-8*t_1^1-3 = 0

t_1^2-8*t_1-3 = 0

DELTA = (-8)^2-(-3*1*4)

DELTA = 76

DELTA > 0

t_1 = (76^(1/2)+8)/(1*2) or t_1 = (8-76^(1/2))/(1*2)

t_1 = (2*19^(1/2)+8)/2 or t_1 = (8-2*19^(1/2))/2

t_1 = (8-2*19^(1/2))/2

x^-1-((8-2*19^(1/2))/2) = 0

1*x^-1 = (8-2*19^(1/2))/2 // : 1

x^-1 = (8-2*19^(1/2))/2

-1 < 0

1/(x^1) = (8-2*19^(1/2))/2 // * x^1

1 = ((8-2*19^(1/2))/2)*x^1 // : (8-2*19^(1/2))/2

2*(8-2*19^(1/2))^-1 = x^1

x = 2*(8-2*19^(1/2))^-1

t_1 = (2*19^(1/2)+8)/2

x^-1-((2*19^(1/2)+8)/2) = 0

1*x^-1 = (2*19^(1/2)+8)/2 // : 1

x^-1 = (2*19^(1/2)+8)/2

-1 < 0

1/(x^1) = (2*19^(1/2)+8)/2 // * x^1

1 = ((2*19^(1/2)+8)/2)*x^1 // : (2*19^(1/2)+8)/2

2*(2*19^(1/2)+8)^-1 = x^1

x = 2*(2*19^(1/2)+8)^-1

x in { 2*(8-2*19^(1/2))^-1, 2*(2*19^(1/2)+8)^-1 }

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