Wednesday: 8 and 34

Problem 8

Difficulty: Functions aren't my favorite, but this one held my interest.

Problem 34

Difficulty: Middling. Fascinating application of algebraic theory.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

answer 08 and answer 34.