2/x=x+4/x^2

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Solution for 2/x=x+4/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)

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

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

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

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

(2*x^1-1*x^3-4*x^0)/(x^2) = 0 // * x^4

x^2*(2*x^1-1*x^3-4*x^0) = 0

x^2

2*x-x^3-4 = 0

{ 1, -1, 2, -2, 4, -4 }

1

x = 1

2*x-x^3-4 = -3

1

-1

x = -1

2*x-x^3-4 = -5

-1

2

x = 2

2*x-x^3-4 = -8

2

-2

x = -2

2*x-x^3-4 = 0

-2

x+2

2*x-x^2-2

2*x-x^3-4

x+2

x^3+2*x^2

2*x^2+2*x-4

-2*x^2-4*x

-2*x-4

2*x+4

0

2*x-x^2-2 = 0

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

DELTA = -4

DELTA < 0

x in { -2} 

x = -2

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