You are Here: Home >< Maths

# Mega A Level Maths Thread MK II Watch

1. (Original post by joostan)
Not quite, because a and b are constants not variables, so saying a=0 is not permissible.
If you consider what type of number is going to be, and what type is going to be what can you deduce?
Spoiler:
Show

3 is a prime number

whilst 2 is also a prime number

-> how can I utilise this

2. (Original post by Robbie242)
Spoiler:
Show

3 is a prime number

whilst 2 is also a prime number

-> how can I utilize this

If I were to say 2 is even, what would you say about ?
And 3? And ?
3. (Original post by joostan)
Dunno what he's after, but yeah, Felix says he's getting somewhere.
Well, alternatively:

Spoiler:
Show

This then gives us the same thing as the RHS, provided that , which is exactly the result we derived using the other method.

Also:

(Original post by joostan)
If I were to say 2 is even, what would you say about ?
And 3? And ?
I believe that Robbie's idea of prime numbers is actually a better way of tackling the question, because it can be extended to cases where both numbers are odd or both even. for example:

Spoiler:
Show

Prove that is irrational.

Assume the opposite i.e.

And we then get to:

Now, your odd and even ideas won't work here. However, you can say that, no matter how many times you multiply 5 by itself, it will never gain a factor of 7 (and vice-versa) so as to derive the contradiction you're after.

4. (Original post by joostan)
If I were to say 2 is even, what would you say about ?
And 3? And
2^a is also even
3^b is not even ?

I'm trying to raise 3 to powers and it keeps coming out odd, is this the contradiction?
5. (Original post by Robbie242)
2^a is also even
3^b is not even ?

I'm trying to raise 3 to powers and it keeps coming out odd, is this the contradiction?
Precisely
6. (Original post by joostan)
Precisely
Got there in the end ahah! its good I'm getting into these problems though, the alevel ones often guide you a lot
7. (Original post by DJMayes)
Well, alternatively:

Spoiler:
Show

This then gives us the same thing as the RHS, provided that , which is exactly the result we derived using the other method.

Basically it's the exact same method, only the complex numbers introduce a greater probability of an algebraic slip up
8. (Original post by Robbie242)
Got there in the end ahah! its good I'm getting into these problems though, the alevel ones often guide you a lot
There's a nice induction one with irrationals if you're interested
9. (Original post by joostan)
There's a nice induction one with irrationals if you're interested
Go on then , I'll at least get past the basis case and the assumption step xd
10. (Original post by joostan)
In essence this is a solution.

was said to be in it's simplest form, which it isn't if both are a multiple of 5
This is a contradiction, so therefore the cubed root of 5 is irrational.
OOHH, so basically in there type of questions you prove that a/b isn't its simplest form, this is means its a contradiction and therefore is irrational? Ahh, so I kind of solved it? :/
11. (Original post by joostan)
Basically it's the exact same method, only the complex numbers introduce a greater probability of an algebraic slip up
I'm not saying it's any better (Although it did actually feel marginally quicker, possibly because I knew what I was going for) but it is an alternative approach using complex numbers which might've been the one Mayman was thinking of.
12. (Original post by Felix Felicis)
Ahh, muy bien

3 hours later on that problem, I think I'm onto something
If it took you that much. That means I could never do it
13. (Original post by Robbie242)
Go on then , I'll at least get past the basis case and the assumption step xd
Prove that:
14. (Original post by DJMayes)
Well, alternatively:

Spoiler:
Show

This then gives us the same thing as the RHS, provided that , which is exactly the result we derived using the other method.

Also:

I believe that Robbie's idea of prime numbers is actually a better way of tackling the question, because it can be extended to cases where both numbers are odd or both even. for example:

Spoiler:
Show

Prove that is irrational.

Assume the opposite i.e.

And we then get to:

Now, your odd and even ideas won't work here. However, you can say that, no matter how many times you multiply 5 by itself, it will never gain a factor of 7 (and vice-versa) so as to derive the contradiction you're after.

Thanks DJ! I will probably use this one as it seems a bit more universal,
i.e. I'd say for my one, no matter how many times you multiply 2 by itself, it will never gain a factor 3, therefore this is a contradiction and hence is irrational
15. (Original post by DJMayes)
I'm not saying it's any better (Although it did actually feel marginally quicker, possibly because I knew what I was going for) but it is an alternative approach using complex numbers which might've been the one Mayman was thinking of.
Yeah, I guess
16. (Original post by joostan)
Prove that:
Explain this notation Lol
17. (Original post by tigerz)
OOHH, so basically in there type of questions you prove that a/b isn't its simplest form, this is means its a contradiction and therefore is irrational? Ahh, so I kind of solved it? :/
Yep
18. (Original post by Robbie242)
Explain this notation Lol
N is the set of natural numbers.
Q is the set of rationals.
The means in

Apologies for misleading you with the primes, you're right it works better
19. (Original post by Robbie242)
Explain this notation Lol
Not entirely sure what all the inequalities are there for, but the final part is saying "is not rational for all natural numbers n".

Also, I would question how appropriate this is for this thread, given that the question you're being asked is in fact Q3 of STEP II, 2003...
20. (Original post by joostan)
N is the set of natural numbers.
Q is the set of rationals.
The means in

Apologies for misleading you with the primes, you're right it works better

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: July 10, 2013
Today on TSR

### Anxious about my Oxford offer

What should I do?

### US couple arrested - 13 children chained up

Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• Poll
Useful resources

Can you help? Study help unanswered threadsStudy Help rules and posting guidelinesLaTex guide for writing equations on TSR

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE