The numbers $1,$ $2,$ $\dots,$ $10$ are to be entered into the 10 boxes shown below, so that each number is used exactly once: P=(◻+◻+◻+◻+◻)(◻+◻+◻+◻+◻).What is the maximum value of $P$? What is the minimum value of $P$?
Hint: Use AM-GM inequality. which states that x+y2≥√xy. (You can prove this with the trivial inequality. )
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