## asnaseer 4 years ago 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

1. lgbasallote

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

2. anonymous

It's a puzzle.

3. asnaseer

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

4. lgbasallote

oh that

5. anonymous

the third to last step

6. anonymous

sqrt of neg?

7. asnaseer

and what exactly is wrong with that step?

8. anonymous

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

9. asnaseer

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

10. anonymous

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

11. asnaseer

correct :)

12. anonymous

you're choosing the positive side

13. anonymous

not the same negative part you're squaring

14. cwrw238

yes - well done frees

15. asnaseer

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

16. asnaseer

well spotted!

17. anonymous

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