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If we solve the equations:
$$x^3+2x^2-9x+2 = 0\\\therefore x = 3, -3, -2\\\therefore x = \pm3, -2$$ $$x^3-4 x^2+9 x-10\\\therefore x = 1+2i, 1-2i, 2\\\therefore x = 1\pm 2i, 2$$ It seems to me that $x = 1 \pm 2i, 2$ would fit better, as we know that it's the complex conjugate, and looks more tidy in both cases.
However my teacher says that it is improper notation, and will sometimes doc a mark if it's a large mark question.

I have also seen it in the data sheet for a few trig equations, such as:
$$\sin(A\pm B)=\sin\!A \cos\!B \pm \cos\!A\sin\!B\\ \cos(A\pm B)=\cos\!A \cos\!B \mp \sin\!A\sin\!B$$ Where the second is expanded into:
$$\cos(A + B)=\cos\!A \cos\!B - \sin\!A\sin\!B\\ \cos(A- B)=\cos\!A \cos\!B + \sin\!A\sin\!B$$
But when I used the same logic, for an answer. Of which I can't remember, which had the answers like:
$$y = (1 \pm x)(2 \mp x) \\\therefore y = (1+x)(2-x), (1-x)(2+x)$$ I was told that the former was wrong, and the latter was the answer.

I'm confused if how I'm using it is allowed, as the only time we use it is when we are solving square-roots, in which it's is implied by the square-root sign.

egreg
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  • If your teacher doesn't like, don't do it. You only risk points and don't really save time. If you are used to that notation and know what is meant by this, I would say it's okay to use it. – Peter Jul 15 '14 at 15:06
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    I have seen answers presented in the way you have written it in maths textbooks before. I would personally have no qualm with it and think your teacher is wrong to mark it down. – lemon Jul 15 '14 at 15:09
  • I have never seen that a product was shortened with this notation. So $y=(1+x)(1−x)(2−x)(2+x)$ cannot be shortened with this notation. – Peter Jul 15 '14 at 15:13
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    @user46944 I would never write $y=(1+x)(1-x)(2-x)(2+x)$ as $y=(1\pm x)(2\mp x)$, but rather interpret $y=(1\pm x)(2\mp x)$ as $y\in{(1+x)(2-x),(1-x)(2+x)}$. Your notation seems really confusing. Moreover, you can easily simplify expressions of that form: $(1+x)(1-x)(2-x)(2+x)=(1-x^2)(4-x^2)$, so there really is no need for a special notation for that. – Joffysloffy Jul 15 '14 at 15:13
  • Your teacher said that the former was wrong probably because the former answer should be rejected for not meeting a given condition. – Mick Jul 15 '14 at 15:16
  • Irrelevant comment: None of $\pm 3$, $-2$ is a root of the first equation. In general I would prefer the $\pm$ notation in order to emphasize symmetries. But mathematical notation has many dialects, and users of one dialect may consider another dialect "wrong." At this time, for this class, there is a need to use the teacher's dialect. – André Nicolas Jul 15 '14 at 15:32
  • Well, we can work backwards, expanding $(x^2-9)(x+2)$, or even more simply not expanding. – André Nicolas Jul 15 '14 at 15:48

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I think your use of $\pm$ is just fine. It seems to be widely used. I was told by one professor that writing things like $$i=1,2,3,4$$ was also improper and that I should rather use $i\in\{1,2,3,4\}$, but I have noticed that a lot of books and professors at my university use the former; including your use of the $\pm$ symbol.
However, if your teacher disagrees and claims to subtract points, you should just follow his notation for now.

Joffysloffy
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