2x^(1/4)=9-(4x^(-1/4))

Solution for 2x^(1/4)=9-(4x^(-1/4)) equation:

D( x )

x < 0

x = 0

x < 0

x = 0

x = 0

x in (0:+oo)

2*x^(1/4) = 9-(4*x^(-1/4)) // - 9-(4*x^(-1/4))

2*x^(1/4)+4*x^(-1/4)-9 = 0

t_1 = x^(1/4)

2*t_1^1+4*t_1^-1-9 = 0

2*t_1^1+4*t_1^-1-9*t_1^0 = 0

(2*t_1^2-9*t_1^1+4*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(2*t_1^2-9*t_1^1+4*t_1^0) = 0

t_1^1

2*t_1^2-9*t_1+4 = 0

2*t_1^2-9*t_1+4 = 0

DELTA = (-9)^2-(2*4*4)

DELTA = 49

DELTA > 0

t_1 = (49^(1/2)+9)/(2*2) or t_1 = (9-49^(1/2))/(2*2)

t_1 = 4 or t_1 = 1/2

t_1 in { 1/2, 4} 

t_1 = 1/2

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

1*x^(1/4) = 1/2 // : 1

x^(1/4) = 1/2

x^(1/4) = 1/2 // ^ 4

x = 1/16

t_1 = 4

x^(1/4)-4 = 0

1*x^(1/4) = 4 // : 1

x^(1/4) = 4

x^(1/4) = 4 // ^ 4

x = 256

x in { 1/16, 256 }