Solve (x^{frac{2}{3}} – 5x^{frac{1}{3}} + 6 = 0).

Explanation

Let (x^{frac{1}{3}} = b) so that the equation is 

((x^{frac{1}{3}})^{2} – 5x^{frac{1}{3}} + 6 = 0)

= (b^{2} – 5b + 6 = 0)

(b^{2} – 3b – 2b + 6 = 0)

(b(b – 3) – 2(b – 3) = 0 implies b = text{2 or 3})

(x^{frac{1}{3}} = 2 implies x = 2^{3} = 8)

(x^{frac{1}{3}} = 3 implies x = 3^{3} = 27)