Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 5.3 AIME, harder Prove it

5. Let $a, b, c, d$ all be positive numbers, prove that: $2 \sqrt{a+b+c+\bar{d}} \geqslant \sqrt{a}+\sqrt{b}+\sqrt{c}+\sqrt{d}$ .

Solution

5. Use the Cauchy inequality to prove.

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