You are Here: Home >< Maths

# MAT question

Announcements Posted on
Would YOU be put off a uni with a high crime rate? First 50 to have their say get a £5 Amazon voucher! 27-10-2016
1. Ive been trying to do this problem but have yet to come up with a solution/answer.
Can I have some help on how to solve this problem?

Is there a positive integer k such that k^3+2k^2+2k+1 is a cube number?
2. (Original post by JackSpinner1)
Ive been trying to do this problem but have yet to come up with a solution/answer.
Can I have some help on how to solve this problem?

Is there an interger k such that k^3+2k^2+2k+1 is a cube number?
I assume the question asks positive integers, since otherwise -1 and 0 are obvious solutions
1)consider k^3
2)consider (k+1)^3
3)remember that those two numbers are consecutive cubes
4)look at the expression again
5)win
3. k=-1...

Posted from TSR Mobile
4. (Original post by apriori1234)
k=-1...

Posted from TSR Mobile
In the original MAT question it's specified k is positive.
5. (Original post by RichE)
In the original MAT question it's specified k is positive.
Lol I would've expected as much

Posted from TSR Mobile
6. (Original post by ValerieKR)
I assume the question asks positive integers, since otherwise -1 and 0 are obvious solutions
1)consider k^3
2)consider (k+1)^3
3)remember that those two numbers are consecutive cubes
4)look at the expression again
5)win
Is the answer no because k^3 is the first cube number and (k+1)^3 = k^3+3k^2+3k+1(which is the next cube number) is not equal to the expression stated and so no postive number would satisfy it.
7. (Original post by JackSpinner1)
Is the answer no because k^3 is the first cube number and (k+1)^3 = k^3+3k^2+3k+1 which is not equal to the expression stated and so no postive number would satisfy it.
you tell me
8. You can show that if then unless .
9. (Original post by JackSpinner1)
Is the answer no because k^3 is the first cube number and (k+1)^3 = k^3+3k^2+3k+1(which is the next cube number) is not equal to the expression stated and so no postive number would satisfy it.
Yes, that basically works.

## Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank
2. this can't be left blank
3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
your full birthday is required
1. Oops, you need to agree to our Ts&Cs to register

Updated: September 14, 2016
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:
Today on TSR

### University open days

Is it worth going? Find out here

Poll
Useful resources

## Make your revision easier

### Maths Forum posting guidelines

Not sure where to post? Read here first

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

Can you help? Study help unanswered threads

## Groups associated with this forum:

View associated groups
Study resources

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

Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.