9x^(-1/2)=x^(1/6)

Solution for 9x^(-1/2)=x^(1/6) equation:

D( x )

x < 0

x = 0

x < 0

x = 0

x = 0

x in (0:+oo)

9*x^(-1/2) = x^(1/6) // - x^(1/6)

9*x^(-1/2)-x^(1/6) = 0

t_1 = x^(1/6)

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

9*t_1^-3-t_1 = 0

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

9*t_1^-4 = 1 // : 9

t_1^-4 = 1/9

-4 < 0

1/(t_1^4) = 1/9 // * t_1^4

1 = 1/9*t_1^4 // : 1/9

9 = t_1^4

t_1^4 = 9 // ^ 1/4

abs(t_1) = 9^(1/4)

t_1 = 9^(1/4) or t_1 = -9^(1/4)

t_1 = 0

t_1 = 0

t_1 = 9^(1/4)

x^(1/6)-9^(1/4) = 0

1*x^(1/6) = 9^(1/4) // : 1

x^(1/6) = 9^(1/4)

x^(1/6) = 9^(1/4) // ^ 6

x = 27

t_1 = -9^(1/4)

x^(1/6)+9^(1/4) = 0

1*x^(1/6) = -9^(1/4) // : 1

x^(1/6) = -9^(1/4)

( -9^(1/4) < 0 i 1/6 in (0:1) ) => x należy do O

t_1 = 0

x^(1/6)+0 = 0

x^(1/6) = 0

1*x^(1/6) = 0 // : 1

x^(1/6) = 0

x = 0

x in { 0} 

x = 27