5z^-4=1/5z^4

Solution for 5z^-4=1/5z^4 equation:

D( z )

z = 0

z = 0

z = 0

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

5*z^-4 = (1/5)*z^4 // - (1/5)*z^4

5*z^-4-((1/5)*z^4) = 0

(-1/5)*z^4+5*z^-4 = 0

5*z^-4-1/5*z^4 = 0

t_1 = z^4

5*t_1^-1-1/5*t_1^1 = 0

5*t_1^-1-1/5*t_1^1 = 0

(5*t_1^0-1/5*t_1^2)/(t_1^1) = 0 // * t_1^2

t_1^1*(5*t_1^0-1/5*t_1^2) = 0

t_1^1

(-1/5)*t_1^2+5 = 0

(-1/5)*t_1^2+5 = 0

DELTA = 0^2-(4*5*(-1/5))

DELTA = 4

DELTA > 0

t_1 = (4^(1/2)+0)/(2*(-1/5)) or t_1 = (0-4^(1/2))/(2*(-1/5))

t_1 = -5 or t_1 = 5

t_1 in { -5, 5} 

t_1 = -5

z^4+5 = 0

1*z^4 = -5 // : 1

z^4 = -5

t_1 = 5

z^4-5 = 0

1*z^4 = 5 // : 1

z^4 = 5

z^4 = 5 // ^ 1/4

abs(z) = 5^(1/4)

z = 5^(1/4) or z = -5^(1/4)

z in { 5^(1/4), -5^(1/4) }