Which Numbers Remain Unchanged When Added or Multiplied by Themselves?

[YesIam]

It may be in here, I don't know...but how many other numbers can you think of that can be added to or multiplied by itself and get the same answer such as 2 and 0? There are others.

 

[Char. Limit]

Numbers that can be added to and multiplied by themselves giving the same answer:

Define the number x. Then, what you're looking for is every x that satisfies:

$$x+x = x*x$$

So...

$$2x=x^2$$

$$x^2 - 2x = x (x-2) = 0$$

Thus, the only two numbers that satisfy this property are 2 and 0.

 

[YesIam]

Well Char, I am sorry but this is the regular 'proof' that some people give and really think that it has to be some kind of proof because they have read it somewhere. I try to always be careful and not say 'always or never'...because if I do I realize that I will usually be wrong. Recall the movie, NEVER SAY NEVER. and the reason for the name. If you just think about this for a minute, when you state something like you did, this means...this is it and nothing else can be true...I just know this is right...no one else can be right because 'I am right', etc. I believe you are working the problem backwards, even if it is a problem. Let's call it Math familiarization-you are not the first to jump to this conclusion and you will probably not be the last, and I can't help that. I first saw this in a book printed in 1943. I remember the date because years later I forgot the solution and had to research though publishers records and buy an 'out of print book'. I still remember the name of the book, the author, the publisher and year. But again, if you just state what you did and not think about anything else, I can't help that. But if you really put some time into reasoning, I think that 'maybe' you can come with some other numbers. When you think, "...only..." you are lost from the start. I would think that some good answers will come in...from some where. I will post another little Math thingie-see what you can do with this, okay.

 

[Evo]

Th OP is either missing information or forgot what the exersize was.