# Intermediate problems (1)

**Algebra**Level 5

I would be posting a series of intermediate-leveled problems for enjoyment.

Find all solutions to the following equations in reals:

\(\frac{1}{x}+\frac{2}{y}+\frac{3}{z}=1\)

\(xyz=162\)

\(|x-|x||+|y-|y||+|z-|z||=0\)

If there are \(n\) solutions are in the form \((x, y, z)=(x_{i}, y_{i}, z_{i}), i=1, 2, 3, …, n\), find \[\sum_{i=1}^n x_{i}\]

This problem is part of the set