t/x=x

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Solution for t/x=x equation: 


D( x )

x = 0

x = 0

x = 0

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

t/x = x // - x

t/x-x = 0

t*x^-1-x = 0

t_1 = x^-1

t*t_1^1-1*t_1^-1 = 0

t*t_1-t_1^-1 = 0

t_1^-1*(t*t_1^2-1) = 0

t*t_1^2 = 1 // : t

t_1^2 = 1/t

t_1^2 = 1/t // ^ 1/2

abs(t_1) = 1/(t^(1/2))

t_1 = 1/(t^(1/2)) or t_1 = -(1/(t^(1/2)))

1/t_1 = 0

1*t_1^-1 = 0 // : 1

t_1^-1 = 0

t_1 należy do O

t_1 = 1/(t^(1/2))

x^-1-(1/(t^(1/2))) = 0

x^-1-t^(-1/2) = 0

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

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

-1 < 0

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

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

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

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

t_1 = -(1/(t^(1/2)))

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

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

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

-1 < 0

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

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

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

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

x in { 1/(t^(-1/2)), 1/(-t^(-1/2)) }

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