r^(3/2)-8r^(1/2)=0

Solution for r^(3/2)-8r^(1/2)=0 equation:

D( r )

r < 0

r < 0

r in <0:+oo)

r^(3/2)-(8*r^(1/2)) = 0

r^(3/2)-8*r^(1/2) = 0

t_1 = r^(1/2)

1*t_1^3-8*t_1^1 = 0

t_1^3-8*t_1 = 0

t_1*(t_1^2-8) = 0

1*t_1^2 = 8 // : 1

t_1^2 = 8

t_1^2 = 8 // ^ 1/2

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

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

t_1 = 0

t_1 = 0

t_1 = 2*2^(1/2)

r^(1/2)-(2*2^(1/2)) = 0

r^(1/2)-2*2^(1/2) = 0

1*r^(1/2) = -(-2*2^(1/2)) // : 1

r^(1/2) = 2*2^(1/2)

r^(1/2) = 2*2^(1/2) // ^ 2

r = 8

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

r^(1/2)+2*2^(1/2) = 0

1*r^(1/2) = -(2*2^(1/2)) // : 1

r^(1/2) = -2*2^(1/2)

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

t_1 = 0

r^(1/2)+0 = 0

r^(1/2) = 0

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

r^(1/2) = 0

r = 0

r in { 8, 0 }