Send help

In the first equation, multiply by $-\sqrt[16]{5}+1$ to cancel out all of the nasty roots and you get $\sqrt[16]{5}x + x = 1$. Simplifying further results in $x = \sqrt[16]{5}-1$ .

Since we want $(x+1)^{48}$, we have $(\sqrt[16]{5})^{48}$, which equals $5^3 = \boxed{125}$

-24