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July 27th, 2016, 08:09 AM   #1
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HMMT really hard problem

Find the largest real number y such that a² + b² + c² + d² ≥ ab + ybc + cd for all real numbers a, b, c and d.

I tried to use the AM-GM Inequality and I found 2 as the answer, but it's wrong! :/
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