Hey guys? look what I discovered!
 

"x+x = x*x" is a possible formula (with x=0,1 or 2) but when I try to simplify this to x I get:

x+x = x*x <=>
(x+x-x)/x = 0 <=>
x/x = 0 <=>
1 = 0

Whoa! I didn't know 1 was equal to 0! Or did I just do something wrong? =D

I am certainly not a mathematician nor even have higher grades in them... But as far as I am concerned, any division can't equal 0...

i suggest you to pay attention in math classes :p

Your first mistake there is in going from the first to the second line.

It should be ((x-x)/x)-x = 0

Which, you may notice, gets you absolutely nowhere towards proving impossible results.

Hey, I was right... I just didn't have the skills to prove it... :worried:

Some can. 0/x = 0 if x /= 0

As for the original equation:

Havell is right, you messed up the second line by saying

(x+x-x)/x = 0

If x+x = x*x, then x+x-x = x^2-x

x = x^2-x

0 = x^2-2x

x^2-2x = 0

x(x-2) = 0 which is possible when and only when x = 0 OR x-2 = 0. The answer is

x = 0 OR x = 2

x = 1 is not a solution.

1+1 = 2

1*1 = 1

1+1 /= 1*1

Know the basics:
http://en.wikipedia.org/wiki/Division_by_zero

Hmmmm, maybe something simplier will be understandable:
http://simple.wikipedia.org/wiki/Division_by_zero

Well, I did say x unequaled zero...

This is because two numbers multiplied giving zero as the result, is possible only if one or both numbers are zero. This in turn means that either x has to be zero or x-2 has to be zero.

Shouldn't it be ((x+x)/x)-x=0? Otherwise the solution would be -1...

In Havell's equation

(x-x)/x-x = 0 | x /= 0

0/x-x=0

0-x = 0

x = 0, which contradicts the statement that x /= 0

So, (x-x)/x-x = 0 has no solution.


Your equation, however, is right only if x /= 0.