# Understand the problem

Let be the lengths of sides of a (possibly degenerate) triangle. Prove the inequality

Let be the lengths of sides of a triangle. Prove the inequality

##### Source of the problem

Caucasus Mathematical Olympiad

##### Topic

Inequalities

##### Difficulty Level

Easy

##### Suggested Book

An Excursion in Mathematics

# Start with hints

Do you really need a hint? Try it first!

The inequality is homogeneous, hence it might be a good idea to make the substitutions etc. The triangle inequality might also come in handy.

As the triangle is allowed to be degenerate, we have . This implies .

Summing, we get . It is possible to use the AM-GM inequality here to get the LHS of the inequality. Also, show that this implies .

Note that by AM-GM. Hence, we get .

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#### Math Olympiad Program

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