Try to figure this one out! How is it possible that two is equal to one, when we all know that that isn’t true. Try to spot the mistake one of the twins made!
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that isnt even an illusion!
man im 12 [primary 6] yet i dunnoe!!! man i’m dumb )’: WAAAA!!!!!!!!!!!!!
Guys, stop thinking so much, the fourth line isn’t equal, distributive property.
(a-b)(a+b) = b(a-b) do the work out
a^2 + b^2 = ab – b^2
the second part equals zero, the first part is a positive number
huh???
this isn’t even an optical illusion…
the mistake there is when 2a=a,
he used that property in equations wherein you transfer a variable to the other side of the equation,
so when you transfer a from 2a to the other side it would be a divide by a which in Algebra is equal to 1.
but the mistake is variables are only equavalent to numbers when they are predefined with a specific no.
This is NOT and OPTICAL ILLUSION. by this logic i could take any math problem….include it in some sort of picture and call it an optical illusion. First..Just because you threw in a picture of two guys does not cover the ‘optical’ requirement in optical illusion. second….This is not an ‘Illusion’ at all. its a math puzzle, a somwhat clever math puzzle yes, but in no way is it an illusion. Unfortunatly more and more of the “Illusions” that have been appearing on this site arent even close to the definition of optical illusion.
I never knew Chuck Norris had a twin, because Chuck Norris can divide by 0.
I really liked this one, it stumpted me for a while. I gotta show this to my Calc teacher.
1=2 sounds like Bush economics.
The only way for 2a to equal a is if they’re both zero. The equation is totally ligitimate, but just cause 2a=a, doesn’t mean 2=1. Also, (a+b)(a-b)=b(a-b), you’re dividing by (a-b), not 0
the algebra in itself is perfect. there is only one problem: the first line:
a=b
which later leads to a division by zero, which is undefineable, and also against the eleventh commandment:
“Thou shalt not divide by zero.”
the reason why this one got so many replies with the correct answers is people enjoy pointing out other people’s errors… and frankly, so do I.
that’s all, people
well, thas it’s true… like the no gravity rule.
>.<
I’m stumped on the first line.
Shouldn’t a = a? The supposed fact that “a = b” is just stupid.
End of story.
And nobody else post about “cant divide by Zero” I’ve read enough of those replies.
even I get this
(a-b)=0
x divided by 0=YOU FAILED MATH CLASS!!
When you divide members of the equation for a factor you have to remove the case when the factor goes zero. so when you divide for a-b you have to remove a-b = 0 from the solutions which is the first equations! so you can’t divide for a-b, because you remove all the solutions!
OK! any given number divided by 0 is not defined therefore the algebraic sequence must come to a halt at that point, as anything after it will be incorrect, hence 2=1! capiche?
step 1 : a=b
step 2 : a2 = ab
but.. if both sides r being squared…
isnt a2 = b2 n not ab?
right??..
so basically .. der is only 1 mistake…
right..or not??
I figured it out. It’s the sum that states “a+b=b”. This is mathematically impossible and with these rules, I can see why the twins think that “2=1″. So the mistake is in the 6th line.
As an engineer and former math teacher I’m saddened to see some of the ignorance displayed here. Taking the whole thing point-by-point (using standard Maple notation) let’s talk about it…
The first line, Let a = b, is perfectly routine and shouldn’t raise any issues.
The second line, multiplying both sides by a, we get a^2 = a*b which is also OK.
In the third line things get very slippery. BY subtracting b^2 from both sides to arrive at a^2–b^2= a*b–b^2 we must recall our premise. Since we are subtracting like terms because a^2=b^2=a*b, we are already in trouble since terms on both sides of our equation are zero! Everything that comes after this step is based on a false premise that IF a*0=b*0 THEN a=b. This is a somewhat subtle use of the zero property over multipication for equations. It is closely related to division by zero.
Factoring terms (we might think) we see that (a+b)*(a-b) = b*(a-b). We’ve now collected our zero into one of our terms, (a-b). This is crucial for the operation of the trick, but we actually left good math behind at step three.
Now the Fait au complet comes in cancelling (dividing) the common (zero) terms on both sides giving us a+b = b (which can only be true for a=b=0, not all possible values of a!)
completing the illusion, the trickster resubstitutes a for b simplifying to 2*a = a (since a = b), and then cancels a to conclude 2 = 1!
Those who opined that the error came in step 4 or between 4 and 5 are close, but must remember that once you have a 0=0 situation (for BOTH RHS and LHS) in ANY equation it is useless. When that happens you must work the math differently. The best way to avoid this pitfall is to use AS FEW TERMS AS POSSIBLE!
Of my last group of AB Calculus students (who scored 3s and 4s on their AP exams) none solved this puzzle! I’ve had three students and 5 colleagues figure it out (correctly) in 23 years of engineering and math teaching. I think the students are doing quite well! They are always better at getting “out of the box.” It’s no wonder the Fields Medals only go to those 40 and younger!
Don’t make it too complicated…
a=0
b=0
That’s all there is to it, basically.
ok, this is where they really really messed up. there were only variables involved before and then suddenly- boom! numbers. real, rational, old-fashioned, numerical, numbers
a=b
asq(a square)=ab
asq-bsq=ab-bsq
(a+b)(a-b)=b(a-b)
2a x 0 = a(a-a)
2a x 0 = 1
a x 0 = 1
1=1
I have not had math in 20 years but whatever I remember from grade 13 indicates that when you multiply a x 0 is always equals 1.
This all makes sense except for the very last line.
a=b or 2=2
a^2=ab or 4=4
a^2-b^2=ab-b^2 or 16-16=16-16 or 0=0
(a+b)(a-b)=b(a-b) or (0+0)*(0-0)=0*(0-0)
(a+b)=b or (0+0)=0
a+a=a or 0+0=0
2a=a or 2*0=0
all true to this point.
But 2*0 does not equal 1
Given that anything multiplied by zero is always equal to zero.
You could say for instance
5 x 0 = 2 x 0
doesn’t mean that 5=2
MacGyver can divide by zero using a candle and a mirror..
This doesnt even make sense because if a=b then a+b cant equal b and a plus a cant equal a makin this whole thing false
I’m not so sure how this is an illusion…
if a=b, then its safe ot say that a and b hold the same value, which is pointless, but just for arguments sake, lets say it fits the scenario, if a is equal to b, then
(a+b) does not = b, it equals 2b
and a + a equal 2 a, so you have 2a = 2b, reduced means a=b, nothing proven.
Plus, in the 4th and 5th lines, im not sure what the author did, but they divided by -0 or something weird like that, because (a-b) becomes (a+b), in which case b on the outside would have become a negative b, which would then make the proof, 1=-1, and technically all numbers are reflexive to their intergers.
It took me a while though to figure this one out, props to the author.
it shouldnt be b(a-b) in the middle step. It should be (b+b)(a-b) which gives you (b+b)(a-b)
if someone already said this, fine, i didnt read past the first 10 really stupid answers.
both are equal to the product ab-b^2, but there is a difference between the two. that is why there is something wrong with it, it has nothing to do with dividing with zero until later on if you decide to continue with it, which you wouldnt because they would look exactly teh same and to simplify you would cancel it all out.
OK. THere are two mistakes, at least one of which has already been said.
#1. if a=b, then a-b=0, and you can’t divide by zero.
#2. If 2a=a, a can only be zero, so you can’t divide by a as the last step.
As a side-note, some people have the wierdest reasons for why it doesn’t make sense. a and b are the first and second lettersof the alphabet? That’s true, but what does it have to do with anything?
In the third line the right side equals 0 because b x b is the same as ab so ab – b squared is 0
What was Annie talking about earlier!?
‘iiii…. am twelve, sixth grade… soooo… yea. It was waay over my head…’
Is she crazy? Oh yeah…I forgot I’m in higher math…lol
I’m eleven and seven months and in sixth grade, and this makes total sense to me!
I’m gonna show my teacher this! ^_^
-EXILE
Exile here! This is what I have to say!
Not sure, but this is what I think:
Problem: What went wrong?
Given: a=b
a^2=ab
a^2-b^2=ab-b^2
(a+b)(a-b)=b(a-b)
(a+b)=b
a+a=a
2xa=a
2=1
a=b we will assume a and b are 2
a^2=ab would be 2×2=2×2 (4)
a^2-b^2=ab-b^2 is 2×2-2×2=2×2-2×2 (0)
(a+b)(a-b)=b(a-b) is (2+2)x(2-2)=2x(2-2) (0)
(a+b)=b is (2+2)=2 (4=2) incorrect
(a+a)=a is (2+2)=2 (4=2) incorrect again
2xa=a is 2×2=2 (4=2) incorrect a third time
2=1 is 2=1
that can’t be right!
Any number but zero is wrong!
If we do try it with 0, however…
a^2=ab would be 0×0=0×0 (0)
a^2-b^2=ab-b^2 is 0×0-0×0=0×0-0×0 (0)
(a+b)(a-b)=b(a-b) is (0+0)x(0-0)=0x(0-0) (0)
(a+b)=b is (0+0)=0 (0) correct
(a+a)=a is (0+0)=0 (0) correct again
2xa=a is 2×0=0 (0) correct a third time
2=1 is wrong. this makes it 0=0
^_^
So technically, 2=1 is wrong, because the only thing possible is 0=0, not to mention variables aren’t neede now that we know it’s 0! Happy trails!
on the line after:
(a+b)=b
the next line written is:
a+a=a
this is impossible as the line should read:
a+b=b
which would make a=0 and b=0
lets start at the line that reads:
(a+b)=b
the next line after that reads:
a+a=a
this is impossible as the next line is supposed to read:
a+b=b
which would make a=0 and in turn making b=0…it is actually really simple cuz the one twim made the mistake…which is what your supposed to look for…duh
Huh?
THE MISTAKE THE TWINS MADE WAS WEARING THOSE CLOTHES.
seeing as you cannot solve an equasion with more then 1 unknown variable, the problem is unsolvable.. most of your explanations would be correct if A and B we’re actually 0, but there’s no way to tell that from the equation a==b. it simply states they’re of equal value
it’s realy simple, the mistake is made in the fifth line, (a+b)= a is wrong (a+b) = a+b so not b
easy problem..any tougher one?!
dude, i learned this crap in 6th grade, this is not ann illusion
i did this in A2A3 math. thats 8th grade stuff. its not that hard.
a squared is a times a not a times b
gothca
Given: a=b
a2 = ab
a2-b2 = ab-b
(a+b)(a-b)= b(a-b) remember given
therefore
(a+b)x 0 = b x 0
0 = 0
LHS = RHS
this guy sure failed math
If half door is open, it is equal to half door shut, therefore if full door is open, it means full door is shut ?!!!
(a-b)=0, therefore (a+b)(a-b)=b(a-b)=0, period.
I know something kind of like this. Three guys walk into an inn and pay ten dollars each for all three of them to stay the night. Later, the clerk realizes he overcharged them and gives five of the dollars to someone to give back to the three men. On the way, the person realizes there is no way to evenly split the five dollars, so he gives one to each of the men and keeps two for himself. So, each of the men only ends up paying nine dollars. Three times nine is twenty-seven. Add the two that the person kept and you get twenty-nine. What happened to the other dollar?
Scott, you have a very good point, but seriously… THIS IS NOTHING TO GET SO WORKED UP OVER!!! Anyway, even if they multiplied by (a-b), the math should still be constant, even if it equals zero. Don’t go all psycho. This really messed up equation is just all in good fun.
i’m in 7th grade and i’m done with algebra 1. if a=b then onthe 4th line then if you use the distributive property then it looks like (a+b)x0=bx0 aka 0=0. case closed. By the way, why the heck did these twins waste their time with this anyway?
Hmm…