+62 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 \(5^3 = \boxed{125}\)
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