[tex]\it x^{\frac{2}{3}}+10=7x^{\frac{1}{3}} \Leftrightarrow (x^{\frac{1}{3}})^2-7x^{\frac{1}
{3}} +10=0
\\\;\\
We\ note\ x^{\frac{1}{3}} =t \ \ and \ the \ equation \ will \ be:
\\\;\\
t^2-7t+10 = 0 \Leftrightarrow t^2 -2t-5t+10=0 \Leftrightarrow t(t-2) -5(t-2)=0[/tex]
[tex]\it \Leftrightarrow (t-2)(t-5)=0
\\\;\\
t-2=0 \Rightarrow t=2 \Rightarrow x^{\frac{1}{3}}=2 \Rightarrow (x^{\frac{1}{3}})^3 =2^3 \Rightarrow x = 8
\\\;\\
t-5=0 \Rightarrow t=5 \Rightarrow x^{\frac{1}{3}}= 5 \Rightarrow (x^{\frac{1}{3}})^3 = 5^3 \Rightarrow x = 125[/tex]
S = {8; 125}
