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Suppose we have the following identity:

(px + (1-p)y)^2 = Ax^2 + Bxy + Cy^2.

Find the minimum of max(A,B,C) over 0 \leq p \leq 1.

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google is your friend:

https://math.stackexchange.com/questions/1967491/suppose-we-have-the-following-identity-px-1-py2-ax2-bxy-cy2-f

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