9x^(1/2)-x^(3/2)=0

Solution for 9x^(1/2)-x^(3/2)=0 equation:

D( x )

x < 0

x < 0

x in <0:+oo)

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

t_1 = x^(1/2)

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

9*t_1-t_1^3 = 0

t_1*(9-t_1^2) = 0

-1*t_1^2 = -9 // : -1

t_1^2 = 9

t_1^2 = 9 // ^ 1/2

abs(t_1) = 3

t_1 = 3 or t_1 = -3

t_1 = 0

t_1 = 0

t_1 = 3

x^(1/2)-3 = 0

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

x^(1/2) = 3

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

x = 9

t_1 = -3

x^(1/2)+3 = 0

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

x^(1/2) = -3

( -3 < 0 i 1/2 in (0:1) ) => x naleu017Cy 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 { 9, 0 }