Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 6.4 National olympiad Prove it

Example 1.3.7. Prove that for all positive real numbers $a, b, c$ , we have
$\frac{a}{b}+\frac{b}{c}+\frac{c}{a} \geq \sqrt{\frac{a^{2}+c^{2}}{b^{2}+c^{2}}}+\sqrt{\frac{c^{2}+b^{2}}{a^{2}+b^{2}}}+\sqrt{\frac{b^{2}+a^{2}}{c^{2}+a^{2}}}$

Solution

None

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