Let a, b, c be positive numbers such that
Prove that there exists a triangle with side lengths a, b and c.
Consider the inequality
where a, b, c are the side lengths of a triangle and k is a real number.
(a) Prove the inequality when .
(b) Find the least value of k such that the inequality holds true for any triangle.
Let a, b, c be positive real numbers. Prove that they are side lengths of a triangle if and only if
for any real numbers p, q, and r such that and .
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