There's an obvious flaw in this. See who's first to spot it. Since the forum text doesn't support superscript, I'm using a^2 to mean a squared
if a = b, then:
a^2 = ab (multiplying both sides by a)
a^2 - b^2 = ab - b^2 (subtracting b^2)
(a - b)(a + b) = b(a - b) (factorising)
(a + b) = b (dividing through by (a-b)
2b = b (because a=b)
2 = 1 (dividing through by b)
Tough one - I was always crap at algebra. I would hazard a guess that a^2 - b^2 and ab - b^2 are both zero. Therefore the only result is 0 = 0 ?
Very close, but that's not quite the line that blows the whole thing up. Let's see if anyone else has a go, before I post the answer.
From the little mathematics I know ...
2 x 0 = 0
1 x 0 = 0
Therefore 2=1
By the way, Paraglider, congratulations on your 300th fan ... any moment now ...
I think your cut-down version is just too simple to fool anyone, but you never know!
Thanks for the fan-observation
a^2 = ab (multiplying both sides by a)
a^2 - b^2 = ab - b^2 (subtracting b^2)
(a - b)(a + b) = b(a - b) (factorising)
(o)(2)= 1(0)
you are dividing 0 by 0
(a + b) = b (dividing through by (a-b)
2b = b (because a=b)
2 = 1 (dividing through by b)
Speak to me in quarter notes. I get that. This ain't no quarter note talk.
LOL
My guess.
The step : "dividing through by (a-b)"
is invalid, because (a-b)=0 and x/0 = undefined
You're exactly right, because the whole premise is that a = b.
And the prize goes to -
Exactly right. Division by zero is undefined (because the result tends towards infinity).
But you must admit it's a neat trick!
No, no, no: I see the obvious flaw here -- Paraglider, it's simple: there's no chocolate in it. Just add chocolate for a perfect equation, every time. Next?
2b, or not 2b? That's the real question.
Assuming a=b is the wrong assunption.
Aww...congrats, Paraglider tis a time to celebrate. Will there be chocolate .... sighs
Oh! I missed out on ^. I was wondering what it was. Poor focus!
The Problem is in the Step 3, you are canceling out (a-b) both on the LHS as well as in the RHS. whereas a=b, and a-b=0, So divide by 0 error, as 0/0 is invalid operation ans will result in 0. As,
0/0= 0*(1/0). Anything multiplied by 0 is 0.
true - dividing by zero is still undefined, even after two months
I like this sort of mental exercises, however I'm crap at maths:) Could you get any easier ones:)
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