how tht can be possible ? is there any error ?

Question

- 6 = - 6 (an assumption)

can be written as

4 -10 = 9 -15

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

(2 - 5/2)^2 = (3 - 5/2)^2 (by opening it we get the same according to (a - b)^2=a^2 + b^2 - 2ab)

2 - 5/2 = 3 - 5/2 (taking 1/2 power on both sides)

2 = 3

how is tht possible ......... isnt date amazing or i m wrong some where ?

Answer 1

(2-5/2) is -1/2, 3-5/2 is +1/2
(-1/2)^2 = (+1/2)^2, but when you take the square root on both sides, you can't take the negative on one side and the positive on the other.
Your second-last step should read
absolute value of (2 - 5/2) = absolute value of (3 - 5/2)
| -1/2| = | +1/2|
1/2 = 1/.2

Answer 2

- 6 = - 6 (an assumption)

can be written as

4 -10 = 9 -15

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

(2 - 5/2)^2 = (3 - 5/2)^2 (by opening it we get the same according to (a - b)^2=a^2 + b^2 - 2ab)

With X^2 = Y^2
Now this only can imply either X = +Y or X= -Y
In your case
(2 - 5/2) = - (3 - 5/2) = -1/2
BUT NOT 2 - 5/2 = 3 -5/2 as you claim
You're like saying
(1/2)^2 = (-1/2)^2 implies 1/2 = -1/2 NOT TRUE !!!

Answer 3

What you are doing is equating the negative square to the positive square root.

In the next to last step 2-5/2 = -(3-5/2)
Now you get the identity -1/2 = -1/2

So be careful when taking square roots and equating them.

Answer 4

your step before the last is false:
2 - 5/2 is not = 3 - 5/2