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# Further Maths Pure As Exam questions Help! watch

1. Hi I am currently doing practice papers in class and I am stuck of a few questions and wondering if you could help.

4) Find the values of a^4 + b^4 + c^4 +abc,
where a, b, c are roots to the equation
U^3 +16U -9=0

Thanks
2. (Original post by Alexia_17)
Hi I am currently doing practice papers in class and I am stuck of a few questions and wondering if you could help.

4) Find the values of a^4 + b^4 + c^4 +abc,
where a, b, c are roots to the equation
U^3 +16U -9=0

Thanks
should be obvious.

Then for , one way would be to consider the fact that all satisfy the cubic, which means we have 3 equations in respectively. Adding these together yields . Note that so we just have

Now multiply both sides by to get , hence manipulate the LHS to obtain something that contains only , , and
3. (Original post by RDKGames)
should be obvious.

Then for , one way would be to consider the fact that all satisfy the cubic, which means we have 3 equations in respectively. Adding these together yields . Note that so we just have

Now multiply both sides by to get , hence manipulate the LHS to obtain something that contains only , , and
Hi,
Thank you for your help. However I am a little confused about how you got to a^3+b^3+c^3+16(a+b+c)+9=0
4. (Original post by Alexia_17)
Hi,
Thank you for your help. However I am a little confused about how you got to a^3+b^3+c^3+16(a+b+c)+9=0
As I mentioned, a,b,c satisfy the cubic. Sub each one into the cubic to get 3 equations. Add the equations.

I.e. a^3+16a-9=0 and the same for b,c
5. (Original post by RDKGames)
As I mentioned, a,b,c satisfy the cubic. Sub each one into the cubic to get 3 equations. Add the equations.

I.e. a^3+16a-9=0 and the same for b,c
I have currently confused on how I could factorise this:

ab^3+ac^3+ba^3+bc^3+ca^3+cb^3
6. (Original post by Alexia_17)
I have currently confused on how I could factorise this:

Proceed.
7. (Original post by RDKGames)

Proceed.
But what would the values be?
8. (Original post by Alexia_17)
But what would the values be?
You can figure those out from the original equation!

Write down the values of , , and by looking at the cubic .

What I wrote in the last post can be reduced to simple a case of these three things.
9. (Original post by RDKGames)
should be obvious.

Then for , one way would be to consider the fact that all satisfy the cubic, which means we have 3 equations in respectively. Adding these together yields . Note that so we just have

Now multiply both sides by to get , hence manipulate the LHS to obtain something that contains only , , and
It looks like they require a^4 + b^4 + c^4 in the question. Or are you giving an example that they can apply to the fourth power sum?
10. (Original post by RDKGames)
x

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