Question

Solve the following equations:
$x^{\frac{2}{n}}+6=5x^{\frac{1}{n}}$.

Answer 1

$x^{\frac{2}{n}}+6=5x^{\frac{1}{n}}$

Put $x^{\frac{1}{n}}=t$

$t^2+6=5t{t}^2-5t+6=0t^2-2t-3t+6=0t(t-2)-3(t-2)=0(t-3)(t-2)=0t=2,3x^{\frac{1}{n}}=t\Rightarrow x=t^{n}x=2^n,3^n$