x^((3)/(2))-3x^((1)/(2))=0

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

D( x )

x < 0

x < 0

x in <0:+oo)

x^(3/2)-(3*x^(1/2)) = 0

x^(3/2)-3*x^(1/2) = 0

t_1 = x^(1/2)

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

t_1^3-3*t_1 = 0

t_1*(t_1^2-3) = 0

1*t_1^2 = 3 // : 1

t_1^2 = 3

t_1^2 = 3 // ^ 1/2

abs(t_1) = 3^(1/2)

t_1 = 3^(1/2) or t_1 = -3^(1/2)

t_1 = 0

t_1 = 0

t_1 = 3^(1/2)

x^(1/2)-3^(1/2) = 0

1*x^(1/2) = 3^(1/2) // : 1

x^(1/2) = 3^(1/2)

x^(1/2) = 3^(1/2) // ^ 2

x = 3

t_1 = -3^(1/2)

x^(1/2)+3^(1/2) = 0

1*x^(1/2) = -3^(1/2) // : 1

x^(1/2) = -3^(1/2)

( -3^(1/2) < 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 { 3, 0 }