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2=1 9/29/09 4:46 PM
Ever have one of those days where the numbers just don't seem to add up? Maybe it's because 2=1. Yeah, you read that right. 2 really does equal 1. Don't believe me? Then I'll prove it:
Take the numbers x and y, and make them equal to each other:
x=y
Multiply both sides of this equation by x:
x²=xy
Subtract y²:
x²-y²=xy-y²
Factor both sides of this equation:
(x+y)(x-y)=y(x-y)
Since the factor (x-y) appears on both sides, divide by (x-y) to get rid of it:
x+y=y
Since x and y are equal, substitute y in place of x:
y+y=y
2y=y
Finally, divide by y:
2=1
See, 2 really does equal 1...or does it?
Take the numbers x and y, and make them equal to each other:
x=y
Multiply both sides of this equation by x:
x²=xy
Subtract y²:
x²-y²=xy-y²
Factor both sides of this equation:
(x+y)(x-y)=y(x-y)
Since the factor (x-y) appears on both sides, divide by (x-y) to get rid of it:
x+y=y
Since x and y are equal, substitute y in place of x:
y+y=y
2y=y
Finally, divide by y:
2=1
See, 2 really does equal 1...or does it?
is this algebra?
Yes, but there's a flaw in the reasoning. Check out the comments below.
yes it's faulty but i loved it!
So did I. Took me a while to figure it out when I first saw it.
If x is equal to y, then you cannot divide both sides by (x-y) because you can never divide something by zero. Good problem, though. I think I will give it to my 8th graders tomorrow!
Very good! I'm not surprised that a teacher would figure it out :)
okay u lost me when you said " take the numbers x and y"!LOL i learned in kindergarden that those were letters!LOL j/k! i use to say the same thing to my algibra teacher! maybe thats why i got a D in that class!LOL
Well, I'm one of those math geeks, so to me, x and y are numbers. Needless to say, that didn't get me too far in English class. lol