Problem #1

There are three parts to this month's challenge:

  1. In the equations below, the squares represent blanks which can be filled with either a plus sign (+) or a minus sign (-). Find a sequence of +'s and -'s that will make the first equation true. Find another sequence that will make the second true.

    Source: USA Mathematical Talent Search

  2. More generally, for which integers a and b can you find a sequence of +'s and -'s to fill in the blanks to make the following true?

  3. What if we replace the square roots by nth roots?

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