Answer:
[tex]x=27,8[/tex]
Explanation:
The equation is
[tex]x^{\dfrac{2}{3}}-5x^{\dfrac{1}{3}}+6=0[/tex]
Let,
[tex]x^{\dfrac{1}{3}}=y[/tex]
So,
[tex]y^2-5y+6=0\\\Rightarrow y=\dfrac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4\times 1\times 6}}{2\times 1}\\\Rightarrow y=3,2[/tex]
[tex]x^{\dfrac{1}{3}}=y\\\Rightarrow y^3=x\\\Rightarrow x=3^3\\\Rightarrow x=27[/tex]
[tex]x=2^3\\\Rightarrow x=8[/tex]
Hence, [tex]x=27,8[/tex].
