The $3 = 2$ trick on Google+ I found out this on Google+ yesterday and I was thinking about what's the trick. Can you tell?

How can you prove $3=2$?
This seems to be an anomaly or whatever you call in mathematics. Or maybe I'm just plain dense.
See this illustration:
$$ -6 = -6 $$
$$ 9-15 = 4-10 $$
Adding $\frac{25}{4}$ to both sides:
$$ 9-15+ \frac{25}{4} = 4-10+ \frac{25}{4} $$
Changing the order
$$ 9+\frac{25}{4}-15 = 4+\frac{25}{4}-10 $$
This is just like $a^2 + b^2 - 2a b = (a-b)^2$. Here $a_1 = 3, b_1=\frac{5}{2}$ for  L.H.S, and $a_2 =2, b_2=\frac{5}{2}$ for R.H.S. So it can be expressed as follows:
$$ \left(3-\frac{5}{2} \right) \left(3-\frac{5}{2} \right) = 
\left(2-\frac{5}{2} \right) \left( 2-\frac{5}{2} \right) $$
Taking positive square root on both sides:
$$ 3 - \frac{5}{2} = 2 - \frac{5}{2} $$
$$  3 = 2 .$$

I think it's something near the root.
 A: On the right side, when you say to take the positive square root of $(2-5/2)(2-5/2)$, you're taking a $-.5 [(2-5/2)]$ instead of $.5$
It's easy to see if you multiply out all the numbers in each step.
A: $2-(5/2)$ is not a positive square root. 
A: HINT $\ $ You erroneously inferred $\rm\ x^2 =\: (-x)^2\ \Rightarrow\ x\: =\: -x\:,\ $ for $\rm\ x\:=\:1/2\:.$
A: Back when I was in academia, I taught the "how to prove stuff" course, and one of the first problems that I'd give (which, I admit, I borrowed from my graduate adviser) was along the same vein, namely:  criticize the "proof" of the following "theorem" or rethink your life!
"Theorem":  You have all the money you need.
"Proof:"  Let $M$ denote the amount of money you have and $N$ denote the amount of money you need.  Let $A=\frac{M+N}{2}$ be the average of $M$ and $N$.  Then, we have:
$2A=M+N$
$2A(M-N)=(M+N)(M-N)=M^2 - N^2$
$M^2-2AM = N^2-2AN$
$M^2-2AM + A^2 = N^2-2AN + A^2$
$(M-A)^2 = (N-A)^2$
And taking the square root of both sides, we have $M-A=N-A$, and hence $M=N$.  $\blacksquare$
A: It's simply not true in the reals that if $ x^2=y^2 $ then x=y.  For example, if $ (-2)^2=2^2 $, but 2 does not equal -2.  The scheme of inference used in the last step in general isn't valid.
