Question

X^(4/3) -5x^(2/3) + 6 =0
Trying to find real solutions.. Any help would be greatly appreciated. I know to get rid of the radical exponent I need to multiply by reciprocal but not sure how to when there are two radicals

Answer 1

cube everything, what does that leave you with?

Answer 2

Put \( u= x^{2/3} \), your equation becomes
\[
u^2-5 u+6 =(u-3) (u-2)=0
\]
The rest is easy

Answer 3

\[
x^{2/3}=2 \implies x= 2 \sqrt 2
\]

Answer 4

\[
x^{2/3}=3 \implies x= 3 \sqrt 3
\]