Problem 6 from the British Maths Olympiad | Inequalities | Math Olympiad Training
This problem comes from the British Maths Olympiad Round 1 in 2010.
Let a, b and c be the lengths of the sides of a triangle. Suppose that ab + bc + ca = 1.
Show that (a + 1)(b + 1)(c + 1) is less than 4.
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