Posted by K. Ventimiglia on November 11, 2002 at 19:48:33:
In Reply to: Re: "Prove" 2=1 : clearer posted by Denis Borris on November 11, 2002 at 07:50:41:
There is another one that I use with my students, Algebra I. It has a little different twist to it.
Let x = 1
Square both sides: x² = 1
Subtract 1 from both sides: x² - 1 = 0
Factor as diff. of 2 squares: (x + 1)(x - 1)=0
Divide by (x-1) to both sides.
Leaves: x + 1 = 0
Replace x with 1 again.
1 + 1 = 0
: let a = b
: a² = ab : Multiply both sides by a
: a² + a² - 2ab = ab + a² - 2ab : Add (a² - 2ab) to both sides
: 2(a² - ab) = a² - ab : Factor the left, and collect like terms on the right
: 2 = 1 : Divide both sides by (a² - ab)
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