Question

Can U disprove the following illustration?
3=2 ??

See this illustration:

-6 = -6
9-15 = 4-10

adding 25/4 to both sides:
9-15+(25/4) = 4-10+(25/4 )

Changing the order
9+(25/4)-15 = 4+(25/4)-10
(this is just like : a square + b square – two a b = (a-b)square.)
Here a = 3, b=5/2 for L.H.S and a =2, b=5/2 for R.H.S.

So it can be expressed as follows:
(3-5/2)** 2 = (2-5/2)** 2

Taking positive square root on both sides:
3 – 5/2 = 2 – 5/2

Cancelling – 5/2 on both sides,

3 = 2

Answer

From,
(3-5/2)^ 2 = (2-5/2)^ 2

The mistake is in
“Taking positive square root on both sides”

LHS = Left Hand Side
RHS = Right Hand Side

For we cannot simply take square roots.
Look at LHS (3-5/2) is the POSITIVE root.
On the RHS (2-5/2) is the NEGATIVE root.
You made them “equal” to get the “wrong proof”.

Actually, to take the roots note that
(2-5/2)^ 2 = (5/2 – 2)^ 2
So, If you wanted to take “positive root” then,
its obviously (5/2 – 2).

Thus comparing positive roots,
3 – 5/2 = 5/2 – 2 which is a identity.