1 is equal to 2

Algebra Level 3

Here is a proof why 1 is equal to 2:

  1. x = y

  2. x * x = y * x

  3. x^2 - y^2 = xy - y^2

  4. (x+y)(x-y) = x-y(y)

  5. x+y = y

  6. y + y = y (remember, x = y)

  7. y = 1; means 2 = 1

Is this right or wrong? If wrong, what step is wrong? For example, if you thought multiplying by x in the beginning was wrong, your answer would be 2.

No Error 4 2 6 Every step is wrong 5 3

Jonathan Hsu by Jonathan Hsu , 19, USA

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2 solutions

Jonathan Hsu
May 11, 2015

by this proof, on step 5, we are dividing by 0, which doesn't work. That means step 5 is wrong

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Ashwin Padaki
May 12, 2015

In step 5, you factored (x - y) from both sides. Since x = y, x - y = 0. So you divided 0 from both sides. FLAWED!!!

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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