- #1

anemone

Gold Member

MHB

POTW Director

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I've come across this delicious problem days ago, and upon trying my very best to solve it for multiple times, I failed each time.

I finally realized this problem is beyond my ability to do it. But I've not given up hope yet, so I want to give it one last try, and MHB is the best place to get for inspiration for solving hard problem such as this one. Hence, I would appreciate it if anyone could take a look at this problem and give me some idea.

Thanks in advance for your help!

Problem:

Find all $a,\,b,\,c\in R$ such that $|ax^2+bx+c|\le1$ for every $-0.5\le x\le 0.5$ and $a^2+b^2+c^2$ is maximum.