How to equate 2=3?

[vsusi]

Do anyone know how to equate 2 = 3 (using square and square root)?

I knew a long back but I forgot this now.

(Just I was betting with my firend.)

Thanks

[SteveCRM]

why'd you bet that 2==3???

the equation has an error in it that usually slips by most people...so at first look they make it look like 2==3

[Destined Soul]

Steve's right. If the proof resulted in 2 = 3, then there would HAVE to be an error (or some violation) in the math to allow this. I remember seeing a proof on 1+1=1 or something like that, and it involved doing something like:

1+1 =1
a+a = b
....
a/(b-a) = something

and then they continued on with the math using the (b-a) as if it was non-zero.

Anyhow, I'm super bored, so I thought I'd share that, and one more thing.

If 2 = 3, then it should be that 2 = 3 = 4 = 5 = ... ??

Oh well, back to work. =P

Destined

[SteveCRM]

I wish that worked on math tests
x = 2

the answer is 265!

but 2 = 265 lol

yeah sorry I'll go now

[Abhishek Reddy]

The proof for 1+1=1 went like this:

Applying a^2 = b^2 + c^2 to an equilateral right-angled triangle, s=1.

Therefore 1^2 = 1^2 + 1^2

1 = 1 + 1

Or something like that...

[SteveCRM]

you can't have an equilateral right triangle

[vsusi]

I know some of you people were curious about whether the question is right or wrong.

I can tell you that the question is correct using Mathematics bug.

Clue: Assume a number. Let us say 2.

1. Square it. (2²= 4)

2. Now take a square root of 4. (It gives two values. +2 and -2)

3. This is a bug in Math. I used only +2. But now I got -2. Now +2 is equalent to -2. If that is equal then 0 = 4 (Am I right)

This will be a simple proof of 0 = 4

2 = 2
Square it
4 = 4
Sq Root it. I can assume +2 on one side and -2 on another side.
2 = -2
When sending 2 to other side
0 = -2 + (-2)

0 = 4


BTW SteveCRM is correct. Pythagoras says a²+b² = c² is for Right angled triange.

[[Digital-X-Treme]]

Originally posted by vsusi
Now +2 is equalent to -2. If that is equal then 0 = 4 (Am I right)

No. 2 is NOT equal to -2.

[vsusi]

Digital-X-Treme

I know that +2 cannot be equivalent to -2.
I would have appreciated if u have given some explanation for ur comment.

Please read it fully?

I have written comments for each line. Please specify the error in the code and explain why.

[Abhishek Reddy]

Right-angled equilateral triangles are obviously impossible. Hence, 1=1+1 is also impossible. It had to be right-angled to be able to apply Pythagoras, and equilateral for the numbers.

It's only meant to bypass the dimmer ones.

[DavidHooper]

vsusi, you are not correct and there is no 'bug' in mathematics.

Here is your argument:
2 = 2
Square it
4 = 4
Sq Root it.
I can assume +2 on one side and -2 on another side.
2 = -2

Here is the correct argument:
2 = 2
4 = 4
Square Root
+-2 = +-2

Your problem is assuming +2 on one side and -2 on another.

[SteveCRM]

in math its not seen as just + or just -, but both.....

+- 2

[boscord]

Originally posted by vsusi


There is no number called +-2 as far as I know. U have to read as + or - 2. Not + and - 2. Only one value.

In math, regardless of whether +2 or -2 are possible solutions, all possible solutions need to be evaluated, rendering +/-2

Out

[simonm]

vsusi

You are talking rubbish.

Just because a number has two roots does not mean that those roots are equivillant, does it?

-2 * -2 = 4
2 * 2 = 4

Therefore,

-2 * -2 = 2 * 2

=> 4 = 4.

What's contradictory about that?

[Bonker Gudd]

How bored must I have been to have come in here and read this thread

[vsusi]

SteveCRM & Others

+-2 is definitely two values. That is how I am proving my equation. ie. +2 and -2. I just said +-2 is not a single value. My argument was a single number cannot have two signs (+ and -)
But u should assume only one value among the two returned.

BTW my Windows 98 calculator is showing single value (2). Is that a Microsoft bug then. Microsoft assumes only one value I think.

Guys I just gave a clue which is similar to what I read some 10 years back. Now I couldn't find that (Mathematics Illusion) book.
I may lose my bet soon.


http://www.dictionary.com/search?q=Square%20root

says

For example, the square roots of 25 are 5 and -5 because 5 × 5 = 25 and (-5) × (-5) = 25.

So there are two values.

[Judd]

vsusi - I think you are being deliberately obtuse to extend a silly theory.

A single finite value cannot have two signs, given. But a square root (or lets say the evaluation of the square root function) can yield two answers. I fail to see why you are then arguing that both of those answers (roots) are equivalent.

Orange trees and apple trees both yield a fruit you can eat.

That doesn't make an apple an orange.

[DavidHooper]

Orange trees and apple trees both yield a fruit you can eat.

That doesn't make an apple an orange.

Chuckle.

I think this topic is stiched up...

[alkatran]

2 does not equal -2
you're equation is so wrong... 4 squared can eqaul either so
2² = -2²

[Dreamlax]

I almost failed a question on a test like this one. It said what is the square root of 18 (this was primary school maths).

So I put
x = 4.24 (2 d.p.)

I was marked wrong and they said the correct answer was +4.24 and -4.24. I told them to get ****ed since the question didn't ask for two roots, it only asked for the square root, which I was taught to (at the same school) assume that the square root of any positive number is positive.

[vsusi]

Area of a square is 36 inch². Find the length of a side.

Answer is -6 inch and +6 inch. LOL.

[nishantp]

Originally posted by vsusi
Area of a square is 36 inch². Find the length of a side.

Answer is -6 inch and +6 inch. LOL.

When relating abstract mathamatical concepts to real life, you have to make certain adjustments, such as discarding negative roots.

[Dreamlax]

If you measure negative 6 inches would the tape measure go inwards?

[mmiill]

no watch this

x^2-4=0

(x-2)(x+2)=0

x=2 or x=-2

BUT!!!!!!

sqrt(4)=+2 and just +2 becouse


sqrt(x^2)=|x| that is Theorem

and when u have sqrt((-2)^2)=sqrt(4) =|-2|=+2 and only +2\

[SteveCRM]

vsusi:

plus OR minus a number....not plus and minus... -2 = -2 or 2 = 2...one or the other

[sql_lall]

a = 1, b = 1
a^2 - b^2 = a-b *Diff. of squares
(a+b)(a-b) = (a-b) *Divide by (a-b)
a+b = 1
1+1 = 1
2=1
=> 2+1 = 1+1, 3=2


BTW:
sqrt(x) MEANS +/- sqrt(x). There are two values for sqrt(x)
=>
4=4,
sqrt(4) = sqrt(4)
THis is as far as you can go.

"sqrt(4)=+2 and just +2 because sqrt(x^2)=|x| that is Theorem"
- note that this only applies when only sqrt(x) is written. i.e. if you see just sqrt(x), this implies the positive root.

[mmiill]

u cant devide whit (a-b) becouse a-b=0

5*0=0
but 5!=1

x*0=0 / :0

=>x=1


and sqrt(x) can be just +.. there isnt two values!!!!

[JungleMan]

Prog_tom can make any equation possible...

[DavidHooper]

Prog_tom can make any equation possible...

Hehe, good joke.

[Dreamlax]

I made up a formula to only show half a parabola (by making negative values result in undefinable answers)... the formula was

y = a * ( (x + |x|) / (x + |x|) ) * ( (x + |x|) / 2 ) ^ 2 + c

If you notice, the first factor (besides a) won't simplify to 1 if x is negative, since you get 0 / 0. The second factor can just be x but I like it to be complicated.

I was proud of doing this... until I found out someone already did it before me.

[Dreamlax]

Originally posted by mmiill
u cant devide whit (a-b) becouse a-b=0

5*0=0
but 5!=1

x*0=0 / :0

=>x=1


and sqrt(x) can be just +.. there isnt two values!!!!

Good point! Not to mention well spotted.

[sql_lall]

For those who had forgotten early on:

Steve's right. If the proof resulted in 2 = 3, then there would HAVE to be an error (or some violation) in the math to allow this. I remember seeing a proof on 1+1=1 or something like that, and it involved doing something like:

1+1 =1
a+a = b
....
a/(b-a) = something

and then they continued on with the math using the (b-a) as if it was non-zero

I was just saying what they were referring to

Also:
"and sqrt(x) can be just +.. there isnt two values!!!! "

But there is two values, i think most people agree that both + and - both are answers.

[DavidHooper]

The convention among mathematicians is that:
sqrt(x) = 4 implies x=2
x^1/2 =4 implies x=+-2

[Dreamlax]

Hold up, if x ^ 0.5 = 4, shouldn't x = 16? And the answer equal +-4?

[DavidHooper]

Sorry! I made a slip of the keyboard. I meant to write:
sqrt(x) = 4 implies x=16
x^1/2 =4 implies x=+-16

<Is quite embarrassed!>

[Dreamlax]

You've done it again! If x is negative, the answer is imaginary!

Also, I finally found the answer which all mathematicians I spoke to agreed to:

Sqrt ( 16 ) = 4   and not -4...

The only way to have two answers is to have a question like this:

Solve for x:
x^2 - 16 = 0

[[Digital-X-Treme]]

The square root of any real number > 0 will always produce two+- real values, as mentioned numerous times in this thread. There's no ifs or buts about it. Its maths. Its just how it is... If people cannot fathom the concept, they should go away and read up on basic algebra, and try to understand further, without coming in here with arguments such as stating 1==2 or the like... </***** over>

This post is being dragged on...

[Dreamlax]

True, for every nth root there are n solutions, including imaginary ones, but if the case was that the square root of a real number equal or above zero is positive or negative, why would the quadratic formula need a +/- sign? Why not just plus... otherwise there would be four solutions, + the positive, - the positive, + the negative, - the negative.

[[Digital-X-Treme]]

I fail to see where you are coming from on the four solution thing... the general form of a quadratic equation is: ax^2 + bx + c

By completing the square on this general form, we arrive at the quadratic formula, which gives us two solutions:

x = (-b + (b^2-4*a*c)^(1/2) ) / 2 * a
x = (-b - (b^2-4*a*c)^(1/2) ) / 2 * a

[DavidHooper]

Dreamlax, oh dear. How feeble. I'm getting too old for this stuff. Just ignore everything I say ok!

[Digital-X-Treme],

If people cannot fathom the concept, they should go away and read up on basic algebra, and try to understand further, without coming in here with arguments such as stating 1==2 or the like... </***** over>

Pretty funny.