# A nice maths trick

Discussion in 'Math' started by amilton542, Nov 27, 2016.

1. ### amilton542 Thread Starter Active Member

Nov 13, 2010
496
64
This is a nice trick question to test your basics. If you've seen these polynomial tricks before don't spoil it. There's a contradiction, can you find it?

Prove $-1 = 2$ given that $4x + 4 = 1 - 2x$

Add x^2 to both sides

$x^2 + 4x + 4 = x^2 -2x +1$

Complete the square

$(x + 2)^2 = (x - 1)^2$

Take the square root

$x + 2 = x -1$

Subtract x

$-1 = 2$

Hint: P*r***e* L**e*

2. ### DGElder Member

Apr 3, 2016
351
87
The roots on each side have two potential solutions, only one can be valid: e.g. (1-x) on the right and (x+2) on the left or (-x-2) on the left and (x-1), either pair reduce to x = -1/2. However, your "hint", P*r***e* L**e*, is a mystery.

Last edited: Nov 27, 2016
3. ### WBahn Moderator

Mar 31, 2012
23,859
7,383
By using the positive root on each side all you have shown is that the choice of the positive roots on each side leads to a contradiction and, hence, is not a valid solution. Starting from your "given" equation, it is clear that the only value of x that need be considered is x = -1/2.

4. ### amilton542 Thread Starter Active Member

Nov 13, 2010
496
64
The hint was parallel lines.

$x + 2 = x - 1$

Parallel lines do not intersect hence there is no solution.

5. ### dannyf Well-Known Member

Sep 13, 2015
2,196
421
not in all geometries.

6. ### MrAl AAC Fanatic!

Jun 17, 2014
5,739
1,213
Hi,

I see two basic problems here.

First, we can not prove that -1=2 because that is a result to a proof already and it is clear that it is false to begin with. So it is false already so nothing to prove. A statement to be proved comes in the form of a question of some kind, like prove the simple 5=x+3 for x=2, where we end up with an equality 5=5 and so we proved it. On the other hand, if we had a question like prove 5=x+3 for x=4 then we end up with an inequality 5<7 or simply 5!=7 so we disproved it. But stating already that -1=2 would be at the end of a proof not at the beginning for most reasonable questions because we already know it is false.

Second, the square root of (x+2)^2 is not x+2, so whatever follows is not correct and therefore any outcome could be incorrect therefore the whole "proof" is invalid. A proof of this type is not something that shows what *might* be true or false it shows what *is* true or false.

Third, there is no good reason why we should try to 'prove' that -1=2 because of some equation that comes from out of nowhere. Equations for proofs come from fundamental natural principles not just any ol' equation we feel like using.

Fourth, for the equation that was given, there is a known solution which has nothing to do with the so called proof

Also, we start with a false statement and end with a false statement, so

Ok, that was more than two basic problems, so try to prove that 2=2+x then for x>0

Granted though this falls into the category of a parlor trick that might be fun for some people who like to try to find out what is wrong with a given proof when the outcome seems so unusual, so it has entertainment value nonetheless.

Last edited: Nov 29, 2016
7. ### dannyf Well-Known Member

Sep 13, 2015
2,196
421
the fact that a^2=b^2 does by itself mean a=b.

thats yoyr fallacy.

8. ### mmoammar New Member

Dec 16, 2016
1
0
No, it does not mean a=b .
There are three solutions:
1) a=0 , b=1 because 0^2=1, 1^2=1
2) a=1 , b=0 for the same reason
3) a=b whatever a,b

9. ### AlbertHall AAC Fanatic!

Jun 4, 2014
7,399
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Or a = -b

mmoammar likes this.
10. ### AlbertHall AAC Fanatic!

Jun 4, 2014
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Zero squared equals one? It didn't when I went to school but I'll grant you that was a long time ago.

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11. ### WBahn Moderator

Mar 31, 2012
23,859
7,383
You might want to rethink case 1 and 2, unless you really are claiming that 0 x 0 = 1.

You might also consider the possibility of a = -b.