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sum (n + 2)\sqrt{a^2 + b^2} >= n(a + b + c + d)

Source: Switzerland - 2015 Swiss MO Final Round p10

January 14, 2023
algebrainequalities

Problem Statement

Find the largest natural number nn such that for all real numbers a,b,c,da, b, c, d the following holds: (n+2)a2+b2+(n+1)a2+c2+(n+1)a2+d2≥n(a+b+c+d)(n + 2)\sqrt{a^2 + b^2} + (n + 1)\sqrt{a^2 + c^2} + (n + 1)\sqrt{a^2 + d^2} \ge n(a + b + c + d)
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