Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 6.2 National olympiad Prove it

Example 8.16 (Vasile) $a, b, c > 0, x = a + \frac{1}{b} - 1, y = b + \frac{1}{c} - 1, z = c + \frac{1}{a} - 1$ , prove that
$x y + y z + z x \geqslant 3$

Solution

None

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None

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