# How to explain this $3=2$ proof? [duplicate]

Possible Duplicate:
The $3 = 2$ trick on Google+

http://www.astahost.com/info/tiiiss-ramanujams-proof-flaws.html

$$-6 = -6$$

$$9-15 = 4-10$$

adding $\frac{25}{4}$ to both sides:

$$9-15+ \Big(\frac{25}{4} \Big) = 4-10+ \Big(\frac{25}{4} \Big)$$

(This is just like : $a^2 – 2ab + b^2 = (a-b)^2$.)

Here $a = 3$, $b=\frac{5}{2}$ for L.H.S., and $a =2$, $b=\frac{5}{2}$ for R.H.S.

So it can be expressed as follows:

$$\Big(3-\frac{5}{2} \Big)^2 = \Big(2-\frac{5}{2}\Big)^2$$

Taking positive square root on both sides:

$$3 - \frac{5}{2} = 2 - \frac{5}{2}$$

$$3 = 2$$

but not clear. Can anybody help me?

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## marked as duplicate by Rasmus, Ｊ. Ｍ., Quixotic, David Mitra, yunoneDec 3 '11 at 12:25

Note: $\displaystyle {\sqrt[n]{a^n} = |a|}$, if $n$ is even and square root is $n=2$.
So, $$2− \frac52=-\frac{1}{2}$$ is not a positive square root making your assumption, and hence, the entire proof, flawed.