This discussion is now closed.

Check out other Related discussions

- how to get better at maths
- Struggling with GCSE maths as a stressed yr 11 student
- Music GCSE 12 Marker
- Revision
- HELP!! Tips for Eduqas Bio A-level
- A-level Mathematics Study Group 2023-2024
- 16+ Sixth form interviews 2022
- Correlation between UKMT Maths challenge and being able to do Maths at Uni
- AQA VS EDEXCEL A-Level Maths
- a levels please help me
- Bebras Oxford University Coding Challenge Looking for Tips
- stuck whether to apply to oxford or cambridge!
- GCSE maths, higher help!!
- ...
- A level math honest review
- Sixth Form Entrance Exam for Top UK Private Schools (Westminster, KCS etc.)
- Oops on walkthroughs
- St Paul's school 16+ entry exam
- Can my MP help with Royal Mail issues?
- maths revision 🙏🙏

Sorry for an unhelpful thread name. Not sure what to call this.

Anyway, I've got a problem with my homework, and I'm really stuck on this question. It reads:

Consider the equation $an^2=182$ where $a$ is any number between 2 and 5 and $n$ is a positive integer. What are the possible values of $n$?

Any help would be much appreciated. The answers are in the back of the book but I'm not sure how to get to them.

It would be easy if a was an integer between 2 and 5, but it says any number.

Thanks,

Bon

Anyway, I've got a problem with my homework, and I'm really stuck on this question. It reads:

Consider the equation $an^2=182$ where $a$ is any number between 2 and 5 and $n$ is a positive integer. What are the possible values of $n$?

Any help would be much appreciated. The answers are in the back of the book but I'm not sure how to get to them.

It would be easy if a was an integer between 2 and 5, but it says any number.

Thanks,

Bon

OK, well I'll assume you're stating the question correctly, even though it does sound quite weird.

Probably the most natural way of solving this is to just look at all the "remotely possible" values for n^2 and see which ones work.

e.g. 20^2 = 400, so an^2 = 182 gives a = 182/400. Since a >=2, this is impossible.

(That's a fairly useless example, but from what I've seen of your ability, I'm sure you can solve this from here, so I didn't want to give any more help).

Probably the most natural way of solving this is to just look at all the "remotely possible" values for n^2 and see which ones work.

e.g. 20^2 = 400, so an^2 = 182 gives a = 182/400. Since a >=2, this is impossible.

(That's a fairly useless example, but from what I've seen of your ability, I'm sure you can solve this from here, so I didn't want to give any more help).

Thanks - I agree, it's a very odd question.

So are you suggesting there's no way of doing it apart from trial and improvement?

I was thinking you could help the trial and error by doing the following:

$\\\displaystyle an^2=182\\ \\n^2=\frac{182}{a}\\ \\n=\frac{\sqrt{182}}{\sqrt{a}}\\ \\n=\frac{\sqrt{2\times 91}}{\sqrt{a}}$

And then say that $\displaystyle \sqrt{91}\ \text {and}\ \sqrt{2}$ must be factors of n? Or does that not work?

So are you suggesting there's no way of doing it apart from trial and improvement?

I was thinking you could help the trial and error by doing the following:

$\\\displaystyle an^2=182\\ \\n^2=\frac{182}{a}\\ \\n=\frac{\sqrt{182}}{\sqrt{a}}\\ \\n=\frac{\sqrt{2\times 91}}{\sqrt{a}}$

And then say that $\displaystyle \sqrt{91}\ \text {and}\ \sqrt{2}$ must be factors of n? Or does that not work?

bon

Ok I realise how stupid that last line is

But you can do better than simple trial and error: n^2 = 400 doesn't work because a ends up too small. Similarly n^2 = 1 doesn't work because a ends up too big. But given you know $2\le a \le 5$ you should be able to find the possible range for n^2. Then just allow for the fact that n is an integer. (e.g. if you found that n^2 > 7, then you know $n \ge 3$).

- how to get better at maths
- Struggling with GCSE maths as a stressed yr 11 student
- Music GCSE 12 Marker
- Revision
- HELP!! Tips for Eduqas Bio A-level
- A-level Mathematics Study Group 2023-2024
- 16+ Sixth form interviews 2022
- Correlation between UKMT Maths challenge and being able to do Maths at Uni
- AQA VS EDEXCEL A-Level Maths
- a levels please help me
- Bebras Oxford University Coding Challenge Looking for Tips
- stuck whether to apply to oxford or cambridge!
- GCSE maths, higher help!!
- ...
- A level math honest review
- Sixth Form Entrance Exam for Top UK Private Schools (Westminster, KCS etc.)
- Oops on walkthroughs
- St Paul's school 16+ entry exam
- Can my MP help with Royal Mail issues?
- maths revision 🙏🙏

Latest

Trending