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

It's a puzzle.

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

oh that

the third to last step

sqrt of neg?

and what exactly is wrong with that step?

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

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

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

correct :)

you're choosing the positive side

not the same negative part you're squaring

yes - well done frees

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

well spotted!

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