Math Puzzles of the Month

Can 2 = 1?

2=1

Here’s our "proof":

Let x = y
so
x² = xy
adding x² to both sides of the equation we get
x² + x² = x² + xy
simplifying we get
2 x² = x² + xy
subtract 2xy from both sides and we get
2 x² – 2xy = x² + xy – 2xy
simplifying we get
2 x² – 2xy = x² – xy
factoring for (x² – xy) we get
2 (x² – xy) = 1 (x² – xy)
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?

Result/Solution(s)

Solution: Can 2 = 1? Math Puzzle

The problem with our proof is in step 8:

8. divide both sides by (x² – xy) we get
2 = 1

In step 1 we said that x = y, so (x² – xy) = 0, and you can’t divide by 0.

Our flawed proof is a good example of why dividing by 0 is not allowed. It’s not just because your math teacher told you so. It is because dividing by 0 can produce impossible results.