1/2x2=1/x-1/2

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Solution for 1/2x2=1/x-1/2 equation: 


D( x )

x = 0

x = 0

x = 0

x in (-oo:0) U (0:+oo)

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

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

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

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

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

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

x^1

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

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

{ 1, -1, 2, -2 }

1

x = 1

x^3+x-2 = 0

1

x-1

x^2+x+2

x^3+x-2

x-1

x^2-x^3

x^2+x-2

x-x^2

2*x-2

2-2*x

0

x^2+x+2 = 0

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

DELTA = -7

DELTA < 0

x in { 1} 

x = 1

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