1/x^2=x

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Solution for 1/x^2=x equation: 


D( x )

x^2 = 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) = x // - x

1/(x^2)-x = 0

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

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

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

x^2

1-x^3 = 0

{ 1, -1 }

1

x = 1

1-x^3 = 0

1

x-1

-x^2-x-1

1-x^3

x-1

x^3-x^2

1-x^2

x^2-x

1-x

x-1

0

-x^2-x-1 = 0

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

DELTA = -3

DELTA < 0

x in { 1} 

x = 1

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