Mathematics - Quadratic Equation Question with Solution | TestHub

Given equation is $x^2-64x+256=0$ whose roots are $\alpha , \beta$.

$\alpha +\beta =64, \alpha \beta =256$
Now ${\left(\frac{{\alpha }^3}{{\beta }^5}\right)}^{\frac{1}{8}}+{\left(\frac{{\beta }^3}{{\alpha }^5}\right)}^{\frac{1}{8}}$
$=\frac{{\alpha }^{\frac{3}{8}+\frac{5}{8}}+{\beta }^{\frac{3}{8}+\frac{5}{8}}}{(\alpha \beta {)}^{5/8}}=\frac{\alpha +\beta }{(\alpha \beta {)}^{5/8}}$
$=\frac{64}{(256{)}^{5/8}}=\frac{64}{32}=2$