Can you prove 3 = 2???

Question

-6 = -6

9 - 15 = 4 - 10

Add 25/4 to both sides.

9 - 15 + 25/4 = 4 - 10 + 25/4

(3)² - 2(5/2)(3) + (5/2)² = (2)² - 2(2)(5/2) + (5/2)²

(3 - 5/2)² = (2 - 5/2)²

Take square root of both sides

3 - 5/2 = 2 - 5/2

Canceling 5/2 from both sides,

3 = 2
?????????????

You get this even if you take negative value of the square root of both sides. (5/2 - 3 = 5/2 - 2)

Crazy or what?

Well, stym, square root of a number can be negative. -2 is also a square root of 4, as -3 is a square root of 9.

If you take negative square root on one side, you must do the same to the other. In case you take negative root:

5/2 -3 = 5/2 - 2

-3 = -2
3 = 2

Out of the four +/- possibilities, two do come up with true equalities, but you can't just dismiss the others! On what basis can you just throw away two of the possibilities, which end in 3 = 2?

Even 4 = 4 has 4 possibilities.

2 = 2
-2 = -2
2 = -2
-2 = 2

How/why do you ignore the last two?


As for the 3 - 5/2 = 0.5 and 2 - 5/2 = -0.5 theory, we have PROVED by working that:

3 - 5/2 = 2 - 5/2
0.5 = -0.5
??????

Answer 1

if the squares of 2 numbers are equal, it does not imply the numbers are equal, which is what you have done.

egample
(-1)^2 and 1^2 both equal 1, but -1 is not equal 1. that is the fault of the argument.
(3 - 5/2)² = (2 - 5/2)²: this says square of 2 numbers =

3 - 5/2 = 2 - 5/2: this says, the numbers are therfore equal, not necessarily true.
in fact, the true equality is, 3 - 5/2 =5/2 - 2

Answer 2

Prove 2 3

Answer 3

Although it looks like you have proven this, you obviously know that 3 does not equal 2. There is one thing you are forgetting in your proof. When you take the square root, you must not forget the positive AND negative square root. Try that again:

Take square root of both sides

±(3 - 5/2) = ±(2 - 5/2)

Now, you'll get 4 possibilities:

1] 3 - 5/2 = 2 - 5/2
2] -3 + 5/2 = 2 - 5/2
3] 3 - 5/2 = -2 + 5/2
4] -3 + 5/2 = -2 + 5/2

Try each of these, and you'll find that not all work.

EDITED:
You can and must throw out the ones that don't work. You know, mathematically, that any number only equals itself. You are allowed to test things in proofs, especially when you come up with multiple answers. In addition, the sign ± implies that it is plus OR minus. Therefore, since it's an OR, you know aht it doesn't have to be both. You test to see which one it actually is. So you're not really throwing it out, but rather, realizing that it's incorrect.

Answer 4

Consider:
(3 - 5/2)² = (2 - 5/2)²

You are saying:
(1/2)^2=(-1/2)^2

Which is true.

There are rules about taking the square root of both sides which are not being followed to reach the conclusion that 1/2=-1/2.

Answer 5

what.

(3 - 5/2)² = (2 - 5/2)²

2-5/2 < 0 so sqrt(2-5/2)² = 5/2-2

3-5/2 = 5/2 -2
3+2= 5/2+5/2
5=5
Not so crazy.


edit.
nice try. Sqrt(4) = -2 or 2 does not mean that -2 = 2
and if you take the negative on both sides you get 5/2-3 = 2 -5/2.
the rule is that sqrt(x²) = abs(x) where abs is the absolute value.

Answer 6

after your square root step you have
3 - 5/2 = 2 - 5/2, or 1/2 = -1/2. False.

Any proof of 2=1, 3=2, etc. contains a problematic step, e.g., dividing by 0, or the one you posited.

Answer 7

This line's false: 3 - 5/2 = 2 - 5/2

3 - 5/2 != 2 - 5/2...because....
3 - 5/2 = 3 - 2.5 = 0.5
2 - 5/2 = 2 - 2.5 = -0.5

Which are not equal, thus (3 - 5/2) and (2 - 5/2) are not equal.

Answer 8

I believe that in order to properly run this equation you must convert the fraction to whole numbers. 25/4 = 6.25. You'll end up with .25=.25

Answer 9

Your square root has problems.

Answer 10

This is a false proof or a paradox. 3 does not equal 2.

And your proof has incorrect mathematical assumptions.