# XYZ! It's easy as abc! :D

Let $$x, y, z$$ be positive numbers such that:

$$(1)$$ $$x = \frac{a}{a+b}$$

$$(2)$$ $$y = \frac{b}{b+c}$$

$$(3)$$ $$z = \frac{c}{c+a}$$

Prove the following:

$$x+y+z > 1$$

Note by Thomas Kim
4 years ago

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Hint: fund $$\frac{1}{x}$$ and similar, apply AM-HM on $$x,y,z$$, and then try to simplify

- 4 years ago