# A fun math equation

Let’s say y=x
Now multiply both sides by x:
xy=x[sup]2[/sup]
Now subtract a y[sup]2[/sup] from both sides:
x
y- y[sup]2[/sup]= x[sup]2[/sup]- y[sup]2[/sup]
Factoring the left side and apply the difference of squares to the right side, we get:
y(x-y)=(x-y)(x+y)
dividing the common terms
y=x+y
since x=y:
y=y+y
y=2y
Or
1=2

I had one of my professors stumped on this one for awhile. It’s a fun one to torment math geeks a little.

Yes, there is an explanation for this, but at least spoiler box your answers for awhile so everyone can enjoy.

Dividing the common term (x-y) must assume x != y (because if they are, the term is = 0, and it doesn’t matter what y or (x+y) are.) Since in your case you’ve posited that x does = y, you shouldn’t be dividing by (x-y)

[SPOILER]

There’s the problem: the common term is (x-y), which = 0 since x=y, so you are dividing by zero.[/SPOILER]

Yeah, you both are correct. But it causes most people more than 4-5 min of head scratching to get.

Well, I’ve seen puzzles similar to this before, and about 90% of the time it involves the same kind of error at some stage in the cvalculation. (The next most common problem is taking square roots, where you assume a positive square root, but the problem really requires the other, negative, root.

Got to concur with Giles on this… it’s the oldest trick in the book. I’m frankly amazed that your math prof. didn’t

1. Know it already – and failing that
2. Pick it up in seconds!

I agree with **Giles ** and Noone Special. This trick has been around for ages. We were shown it when I was at school in the 70s. I’m surprised that any maths teacher would be stumped by it.

It only took me a minute or so, because I saw it…on the Dope!

I may have been misleading, but the professor that was stumped was not a math prof. He was a Mechanical Engineering Prof and certainly knew the math - but I guess he’d never seen this trick.

I hadn’t seen it until my senior year in college, and I was stumped (at least for a little while).

Doesn’t that essentially make the equation 0=0?

I’m STILL scratching my head, and it has been past 10 mins. After I post this, i’m peeking at the spoilers.

:: Divide By Zero Error ::
:: Please Reboot Universe ::

The title of this thread is an oxymoron.

Why? Why is “Fun Math” incompatible with “Equation?”

I think that you segmented the phrase at the wrong place. I think that Elendil’s Heirthe was alluding to the incompatibility between “Fun” and “Math Equation”. But I disagree. Math can be fun, but the solution to this thread’s particular math puzzle is so well known that it was indeed no fun.

For a rollicking good time, you need Euclid’s Theorem. That’s cute.

Take the integral of 1/x, wrt x by integrating by parts. (But I know the answer is ln(x), you say. I know you know that. Just go with me on this.)

u=1/x
dv=dx

So du=-1/x^2
and v=x

int(u dv) = u*v - int(v du)

int(dx/x) = 1 + int(dx/x)
Subtract that original integral from both sides.
0=1

[spoiler]The formula SHOULD say

int(u dv) = u*v - int(v du) + C

Or at least you need to recognize that when you solve int(v du), you need to stick a +C on whatever you get. The point is, don’t forget the +C!!!

In this case, C=-1, so we get 0=0[/spoiler]

Ok, so I’m pretty new here, but was this a woosh, or did I get double-wooshed?

It was a whoosh.

Unless I’m triple-whooshing you :).

I’d heard of the equation in the OP, too, which can be fun if you show it to someone who hasn’t seen it before. But my favourite is still the derivation of women = all evil :).

I saw this in print in the 60’s.

(Sob - I’m old!)