2 = 1? Explain please,Prof. Hafiz..

Given

Multiply both sides by X

Subtract Y^2 from both sides

Factor both sides

Cancel out common factors

Substitute in from line (1)

Collect the Y's

Divide both sides by Y

Now obviously, 2 doesn't equal 1. So what's wrong with this proof?




Answer
'Cancelling' the common factors from line (4) to (5) means dividing by the factor (X-Y). Since X=Y, this is a division by 0, the results of which are undefined.

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