Thread: O/T: What is wrong here?
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dpb dpb is offline
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Default O/T: What is wrong here?
On 05/12/2015 4:41 PM, wrote:


Let: a = b,
Then: (1) a^2 = ab,
(2) a^2 - b^2 = ab - b^2,
(3) (a + b)(a - b) = b(a - b),
(4) a + b = b,
(5) 2b = b,
(6) 2 = 1

It would seem that we have proved 2 = 1.

What is wrong here?

The problem is in line 3. ...
....
Also to allow the equation to be balanced, you need to apply the
same values and operations to both sides of the equation. In #3, you
have (a+b) x (a-b) on the left. On the right it's b x (a-b). The
equation is NOT equal at this point. And as I mentioned before (a-b)
is zero.

Nope--thru (3) everything is ok... (3) is simply factoring (2)

(a-b)*(a+b) = a^2 + ab - ab - b^2; the two ab terms of alternate sign
cancel leaving -- a^2 - b^2

The RHS is also legitimate irrespective of what a, b actually are;
multiplication is associative so taking the one 'b' out to the outside
of the factor (a-b) is ok. As you noted, substituting values here
yields 0=0 so that's ok.

The problem doesn't come until (4) when divide out the (a-b) term. ["You
can't do that!!!!"] Until then all is well...

Do I win something?

Sorry, not this time...

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