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I went to a mini-reunion with a few friends from my high school class up in Chicago last weekend (and got caught in the blizzard on the way back, but that's another story.)

I was reminded of the math that we did in high school, and what fun and challenge it was. Here's a problem from ninth grade:

Q: Given

x² + y² ≤ 1,

show that

|x² + 2 x y - y²| ≤ √ 2  .

Can your ninth grader solve this problem?