x^(5/2)-64x^(1/2)

Solution for x^(5/2)-64x^(1/2) equation:

D( x )

x < 0

x < 0

x in <0:+oo)

x^(5/2)-(64*x^(1/2)) = 0

x^(5/2)-64*x^(1/2) = 0

t_1 = x^(1/2)

1*t_1^5-64*t_1^1 = 0

t_1^5-64*t_1 = 0

t_1*(t_1^4-64) = 0

1*t_1^4 = 64 // : 1

t_1^4 = 64

t_1^4 = 64 // ^ 1/4

abs(t_1) = 2*4^(1/4)

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

t_1 = 0

t_1 = 0

t_1 = 2*4^(1/4)

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

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

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

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

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

x = 8

t_1 = -(2*4^(1/4))

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

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

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

( -2*4^(1/4) < 0 i 1/2 in (0:1) ) => x należy do O

t_1 = 0

x^(1/2)+0 = 0

x^(1/2) = 0

1*x^(1/2) = 0 // : 1

x^(1/2) = 0

x = 0

x in { 8, 0 }