Question

I need help. this is the problem x^2/3+10=7x^1/3

Answer 1

`\it x^{(2)/(3)}+10=7x^{(1)/(3)} \Leftrightarrow (x^{(1)/(3)})^2-7x^{\frac{1} {3}} +10=0 \\\;\\ We\ note\ x^{(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`


`\it \Leftrightarrow (t-2)(t-5)=0 \\\;\\ t-2=0 \Rightarrow t=2 \Rightarrow x^{(1)/(3)}=2 \Rightarrow (x^{(1)/(3)})^3 =2^3 \Rightarrow x = 8 \\\;\\ t-5=0 \Rightarrow t=5 \Rightarrow x^{(1)/(3)}= 5 \Rightarrow (x^{(1)/(3)})^3 = 5^3 \Rightarrow x = 125`

S = {8; 125}