Here’s our “proof”

1. Let x = y
2. so
   x² = xy
3. adding x² to both sides of the equation we get
   x² + x² = x² + xy
4. simplifying we get
   2 x² = x² + xy
5. subtract 2xy from both sides and we get
   2 x²– 2xy = x² + xy – 2xy
6. simplifying we get
   2 x²– 2xy = x²– xy
7. factoring for (x²– xy) we get
   2 (x²– xy) = 1 (x²– xy)
8. divide both sides by (x²– xy) we get
   2 = 1

Since 2 can’t equal 1 there must be something wrong here. What’s wrong with our proof?

After you’ve thought about it check our solution.

Thanks to Renato Mello for this month’s puzzle.

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