Here is the proof...

(1) X = Y | Given |

(2) X^{2} = XY | Multiply both sides by X |

(3) X^{2} - Y^{2} = XY - Y^{2} | Subtract Y^{2} 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.