Proof 2+2=5

Proof 2 + 2 = 5

I think this is the misstep!

Equating Negative Number To Positive Numer

Proof : 2 + 2 !=5

Look what is done under square roots in red rectangles. At first, 4 - 9/2 = - 1/2 is squared to 1/4 & at second while taking square root of same 1/4, it's taken as + 1/2. So -1/2 converted to +1/2 by squaring followed by taking square root. This is certainly not 'fair' mathematically!

Actually square root of (5-9/2)^2 should have been - (5-9/2) = - 1/2!

Here is that attempt! 

Proof 2 = 1

Can you figure out misstep in above?

Here it is figured out! 

How Proof : 2 = 1 is Wrong

What was allowed?

Since a = b, then a - b = 0.

So we can't divide both sides by (a - b) on both sides to eliminate (a -b) since division by 0 is not defined or infinity!