Here is the proof...
| (1) X = Y | Given |
| (2) X2 = XY | Multiply both sides by X |
| (3) X2 - Y2 = XY - Y2 | Subtract Y2 from both sides |
| (4) (X+Y)(X-Y) = Y(X-Y) | Factor both sides |
| (5) (X+Y) = Y | Cancel out common factors |
| (6) Y+Y = Y | Substitute in from line (1) |
| (7) 2Y = Y | Collect the Y's |
| (8) 2 = 1 | Divide both sides by Y |
Since X = Y,
ReplyDelete(X+Y)(X-Y) = Y(X-Y) --- (1)
(X+Y)(0) = Y(0)
0 = 0
You cannot cancel the common factors of (X-Y) from (1)
So the error lies in step 4 to 5.
Interesting post. Very intriguing.
The problem is in step 4.
ReplyDeleteYou multiply both sides by (x-y). As x = y, you are multiplying by zero.
Multiplying by zero always yields magical results.
That's right. You can't divide by zero! That's always a mistake.
ReplyDeleteI'm glad you found it interesting steph.