Question

x^(5/6)-6x^(5/12)+9=0

Answer 1

basically, this is a quadratic equation

\[(x^{\frac{5}{6}})^2 -6x^{\frac{5}{6}} + 9 = 0\]

and I can tell you its a perfect square.

hope it helps

Answer 2

\[ \large
x^{5/6}-6x^{5/12}+9=0 \\ \large
(x^{5/12})^2 - 6x^{5/12}+9=0 \\ \large
~~~~t^2~~~ - ~~~~6t~~~~+~~~9 = 0 ~~~ \text{where } t = x^{5/12}\\ \large
\]

Answer 3

Solve the quadratic in t.
Then put back t = x^{5/12} and solve for x.

Answer 4

oops sorry about the mistake