asnaseer Group Title 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 one year ago one year ago

1. lgbasallote Group Title

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

2. Freyes Group Title

It's a puzzle.

3. asnaseer Group Title

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

4. lgbasallote Group Title

oh that

5. Freyes Group Title

the third to last step

6. JakeV8 Group Title

sqrt of neg?

7. asnaseer Group Title

and what exactly is wrong with that step?

8. Freyes Group Title

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

9. asnaseer Group Title

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

10. Freyes Group Title

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

11. asnaseer Group Title

correct :)

12. Freyes Group Title

you're choosing the positive side

13. Freyes Group Title

not the same negative part you're squaring

14. cwrw238 Group Title

yes - well done frees

15. asnaseer Group Title

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

16. asnaseer Group Title

well spotted!

17. oldrin.bataku Group Title

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