Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 6.2 National olympiad Prove it

43. Let $a, b, c$ be positive numbers, and $a+b+c=1$ , prove: $\frac{a^{2}}{b}+\frac{b^{2}}{c}+\frac{c^{2}}{a} \geqslant 3\left(a^{2}+b^{2}+c^{2}\right)$ .

Solution

None

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