Hi All,
Even though this is wildly off topic, this signature has been annoying me while lurking through. Hopefully this hasn't been discussed before.
Here is something to relieve stress.
Assume that a does not equal b.
a + b = t
(a + b)(a - b) = t(a - b)
a - b = at - bt
a - at = b - bt
a - at + t/4 = b - bt + t/4
(a - t/2) = (b - t/2)
a - t/2 = b - t/2
a = b
Since all numbers are the same, math is useless.
The error in logic falls between the line (a - t/2) = (b - t/2)
and a - t/2 = b - t/2. The square function, f, is not linear.
i.e. f(a)=f(b) does not necessarily imply a = b.
An example of this is (-3)^2 = (3)^2, yet it goes without saying that -3 does not equal 3.
With a + b = t, a - t/2 simplifies to a/2 - b/2, with b - t/2 simplifying to b/2 - a/2. Given that a does not equal b, it is obvious that one of the terms is positive while the other is negative.
If you multiply one side by the corrective negative sign.
One obtains
a - t/2 = -(b - t/2)
a - t/2 = -b + t/2
a + b = t, which is the initial relationship.
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