Math Is Fun Forum

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What was your method for solving the four simultaneous equations bobbym? I have now done it, but it took me multiple pages!!

I got twelve by following it round, almost as if it were a clock, but then I noticed that there are other ways (e.g. left, up, left). I'm sure there's a way to be sure (this isn't really my area of expertise) but just a cursory attempt at a brute force solution seems to suggest to me that 16's a pretty good answer.

Hmmmm....on second thought, maybe? I'm not sure. My original thinking was that when the first ± is +, so is the second one and when the first ± is -, so is the second one. So, for example:

When the first ± is +, so is the second one and when the first ± is -, so is the second one. So we have:

Hence the need for a ∓ sign. In this case we would have +(+5) or -(-5) and only these options. But it seems reasonable to be able to say:

So, yes, I think you're right. Ignore my second post. The first one still stands, though, I think

But yes, anonimnystefy is right. Sorry for confusing the matter further, the important thing to note is √x is always the positive, principal root, hence the need for the ± sign before the radical sign.

I would imagine it dates back to early geometry. If, say, you're trying to calculate the length of a hypotenuse, you're not interested in the negative values. I imagine this general precedence of the principal square root was incorporated into the notation when it was defined. Because, of course, we define our notation to be useful to us and easy to work with. But, without realising it, you've always been using the convention whenever you've gone:

If it weren't for the fact that the √ sign only referred to the principal value, you wouldn't need the ±, that would be implied by the √. Then you could just write:

It's just the way we learn to think about it conceptually

Excellent technical observation, we should, really, say that:

However, it is true to say that the square root of 9 is plus or minus 3. The problem we have is that the sign √ refers to the principal square root only.

This does make the thing a little harder to understand, though

Suffice it to say that when we square root both sides of an equation, we must include the ± sign, as an equation of the form:

Has two solutions.

Sorry, posted that before I saw bob bundy had done the same thing

Okay, well, thank you very much, both of you, that's all i needed

Bobbym that's fantastic, thank you!

That's no problem, I'm not in a rush