a/x=b2x

Solution for a/x=b2x equation:

D( x )

x = 0

x = 0

x = 0

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

a/x = b^2*x // - b^2*x

a/x-(b^2*x) = 0

a*x^-1-(b^2*x) = 0

t_1 = x^-1

a*t_1^1-b^2*t_1^-1 = 0

a*t_1-(b^2*t_1^-1) = 0

t_1^-1*(a*t_1^2-b^2) = 0

a*t_1^2 = b^2 // : a

t_1^2 = (b^2)/a

t_1^2 = (b^2)/a // ^ 1/2

abs(t_1) = b/(a^(1/2))

t_1 = b/(a^(1/2)) or t_1 = -(b/(a^(1/2)))

1/t_1 = 0

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

t_1^-1 = 0

t_1 naleu017Cy do O

t_1 = b/(a^(1/2))

x^-1-(b/(a^(1/2))) = 0

1*x^-1 = a^(-1/2)*b // : 1

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

-1 < 0

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

1 = a^(-1/2)*b*x^1 // : a^(-1/2)*b

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

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

t_1 = -(b/(a^(1/2)))

b/(a^(1/2))+x^-1 = 0

1*x^-1 = -(a^(-1/2)*b) // : 1

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

-1 < 0

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

1 = -a^(-1/2)*(-b)*x^1 // : -(a^(-1/2)*b)

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

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

x in { 1/(a^(-1/2)*b), 1/(-(a^(-1/2)*b)) }