1 = 2 Proof

What step is incorrect?

Step 1: Let A A = B B

Step 2: Then A 2 A^2 = B 2 B^2

Step 3: A 2 A^2 + A 2 A^2 = A 2 A^2 + A B AB

Step 4: 2 A 2 2A^2 = A 2 A^2 + A B AB

Step 5: 2 A 2 2A^2 - 2 A B 2AB = A 2 A^2 + A B AB - 2 A B 2AB

Step 6: and 2 A 2 2A^2 - 2 A B 2AB = A 2 A^2 - A B AB

Step 7: This can be written as 2 ( A 2 2(A^2 - A B ) AB) = 1 ( A 2 1(A^2 - A B ) AB)

Step 8: and cancelling the ( A 2 (A^2 - A B ) AB) from both sides gives 1 = 2

7 2 1 5 6 4 8 3

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1 solution

Micah Gadbois
Jul 17, 2017

Step 8 . We cannot divide by A 2 A^2 - A B AB . That equals 0, dividing by 0 is undefined. 1 = 2 is undefined.

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