# 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

Intermediate Problems

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