Did I just break math?

[Obnoxious]

Observe:

2 = 2

2² = 2²

4 = 4

Unsquare both sides, and you get either

2 = 2 or -2 = 2

And if you square both sides again, you get

4 = 4 again

So, does -2 = 2? Or am I just an idiot?

[ecoli]

taking the square root of both sides would yield 2=2 and -2=-2

[Obnoxious]

but -2 = 2 also comes out as a possibility.

[calbiterol]

sorry, it doesn't work that way - both sides are going to be +/- 2... that's just the way it is...

[Callipygous]

you just broke our presentation of math. the fact is -2 does not equal 2 (obviously). just because the answer could be -2 and 2 does not mean that it actually works. when solving this in a real life equation if you left it at that, instead of plugging things in (or using logic) to remove one of the answers you would get a big fat "0". try telling your teacher its -2 feet some time.

[ydoaPs]

you can if you are taling about trig:)

[Dak]

the equasion reads "plus or minus 2" = "plus or minus two", which is correct as both sides of the equasion are equal

 

to keep it an equity, you have to do the same things to both sides, right? so you cant just take the modulouse of one side and the modulouse*-1 of the otherside to get 2 = -2.

 

so for example,

 

4 = 4,

[math] \sqrt{4} = \sqrt{4}, [/math]

+or- 2 = +or- 2,

4 = 4,

 

heres a better one, as far as proving the incorrect goes:

 

 

a = b

(times by a gives)

[math]a^2 = ab [/math]

(minus [math]b^2[/math] gives)

[math]a^2 - b^2 = ab - b^2[/math]

(bracketise (forget the correct term, sorry))

(a + b)(a - b) = b(a - b)

(now divide by (a - b))

a + b = b

(now, as a = b, substitute b for a to get)

b + b = b

(ie)

2b = b

(divide by b)

2 = 1

 

tada!

 

its not correct, but it seems like i, too, have broken math.

[ydoaPs]

another unknown error. what is going on?

[Dak]

my fault: 1st time using [math] \LaTeX [/math]

 

hang on, ill fix my last post

 

:::EDIT::: hmm, well athetics aside atleast its readable now

[ed84c]

Observe:

2 = 2

2² = 2²

4 = 4

Unsquare both sides' date=' and you get either

2 = 2 or -2 = 2

And if you square both sides again, you get

4 = 4 again

So, does -2 = 2? Or am I just an idiot?[/quote']

 

wack off a google image search for quadratic parabola

[Klaynos]

When the +/- sign is used on both sides of an equation (eg in double angle trig identities) it is taken that if + is chosen on one side + is chosen on the other side, BUT it is possible (also in double angle trig identities there is an exaple of this) is to have a -/+ sign on one side and +/- on the other in which case you pick + on one side and - on the other.

 

So in the case of a squar rout it is always written as +/- so one is picked and used on both sides...

[mmalluck]

Dak: You divide by (a-b), but from the very begining a=b, so when you are dividing (a-b) you are dividing by zero. That's a big math no-no. Ta da!

[Dak]

yup! nice1. took me absolutely ages to spot that one when i first saw it

 

there are a couple more on this site, inclluding another x = -x one involving square-roots like the OP