(x^(3)*x^(4))^2a/(x^5)^3=x^13

Solution for (x^(3)*x^(4))^2a/(x^5)^3=x^13 equation:

D( x )

(x^5)^3 = 0

(x^5)^3 = 0

(x^5)^3 = 0

1*x^15 = 0 // : 1

x^15 = 0

x = 0

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

(a*(x^3*x^4)^2)/((x^5)^3) = x^13 // - x^13

(a*(x^3*x^4)^2)/((x^5)^3)-x^13 = 0

a*x^-1-x^13 = 0

t_1 = x^-1

a*t_1^1-1*t_1^-13 = 0

a*t_1-t_1^-13 = 0

t_1*(a-t_1^-14) = 0

-1*t_1^-14 = -a // : -1

t_1^-14 = a

-14 < 0

1/(t_1^14) = a // * t_1^14

1 = a*t_1^14 // : a

1/a = t_1^14

t_1^14 = 1/a // ^ 1/14

abs(t_1) = 1/(a^(1/14))

t_1 = 1/(a^(1/14)) or t_1 = -(1/(a^(1/14)))

t_1 = 0

t_1 = 0

t_1 = 1/(a^(1/14))

x^-1-(1/(a^(1/14))) = 0

x^-1-a^(-1/14) = 0

1*x^-1 = a^(-1/14) // : 1

x^-1 = a^(-1/14)

-1 < 0

1/(x^1) = a^(-1/14) // * x^1

1 = a^(-1/14)*x^1 // : a^(-1/14)

1/(a^(-1/14)) = x^1

x = 1/(a^(-1/14))

t_1 = -(1/(a^(1/14)))

1/(a^(1/14))+x^-1 = 0

1*x^-1 = -a^(-1/14) // : 1

x^-1 = -a^(-1/14)

-1 < 0

1/(x^1) = -a^(-1/14) // * x^1

1 = -a^(-1/14)*x^1 // : -a^(-1/14)

1/(-a^(-1/14)) = x^1

x = 1/(-a^(-1/14))

t_1 = 0

x^-1+0 = 0

x^-1 = 0

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

x^-1 = 0

x należy do O

x in { 1/(a^(-1/14)), 1/(-a^(-1/14)) }