If and are two roots of x^2-64x+256=0, then the value of ^3/8^5/8+^3/8^5/8 is:

Question

If $\alpha$ and $\beta$ are two roots of $x^2-64x+256=0$, then the value of $\alpha^{3/8}\beta^{5/8}+\beta^{3/8}\alpha^{5/8}$ is:

Accepted Answer

$\alpha+\beta=64$, $\alpha\beta=256=2^8$.

$$\alpha^{3/8}\beta^{5/8}+\beta^{3/8}\alpha^{5/8}=\frac{\alpha+\beta}{(\alpha\beta)^{5/8}}=\frac{64}{(2^8)^{5/8}}=\frac{64}{32}=2.$$

Solutions · 1