Puzzle: Who can spot what is wrong here?
Theorem: 4 = 5
Proof: -20 = -20
16 - 36 = 25 - 45
4^2 - (9x4) = 5^2 - (9x5)
4^2 - (9x4) + 81/4 = 5^2 - (9x5) + 81/4
(4 - 9/2)^2 = (5 - 9/2)^2
4 - 9/2 = 5 - 9/2
4 = 5

Question

Puzzle:    Who can spot what is wrong here?
Theorem:             4 = 5
Proof:               -20 = -20
                  16 - 36 = 25 - 45
            4^2 - (9x4) = 5^2 - (9x5)
4^2 - (9x4) + 81/4 = 5^2 - (9x5) + 81/4
            (4 - 9/2)^2 = (5 - 9/2)^2
                  4 - 9/2 = 5 - 9/2
                            4 = 5

lgbasallote · Answer

how did you get -20=-20 from 4=5

anonymous · Answer

It's a puzzle.

asnaseer · Answer

The Theorem states 4 = 5
It is then followed by the proof

lgbasallote · Answer

oh that

anonymous · Answer

the third to last step

anonymous · Answer

sqrt of neg?

asnaseer · Answer

and what exactly is wrong with that step?

anonymous · Answer

The step is squaring a negative 1/2 and the other is squaring 1/2

asnaseer · Answer

which is fine, since (-1/2)^2 = (1/2)^2

anonymous · Answer

Yes but then the square root of that after is where the problem is

asnaseer · Answer

correct :)

anonymous · Answer

you're choosing the positive side

anonymous · Answer

not the same negative part you're squaring

cwrw238 · Answer

yes - well done frees

asnaseer · Answer

it is essentially the same as saying:

                (-1)^2 = (1)^2
therefore        -1 = 1

asnaseer · Answer

well spotted!

anonymous · Answer

$$\pm[4-\frac92]=\pm[5-\frac92]$$