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[FP2 AQA] Help with roots of a cubic and with summations watch

1. Hello!

I was working on these questions yesterday:

https://www.dropbox.com/sh/x2qs0oe7a...IdhTgfx2a?dl=0

I don't understand why in (3a), the numerator cancels to . Can someone explain this to me?

Also, I don't understand the method the mark scheme uses to prove that (4b) is true, I would have expanded the summation of a^3 + b^3 + y^3 and equated it with 3aby but this would have taken ages for a 3 mark question. Can someone explain the intermediate steps in the mark scheme answer?

I'm probably being stupid and missing the obvious so help is very much appreciated! Thanks.
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2. When you expand the brackets you should and simplify, you should get r2^r+1-r2^r, have you gotten to that stage?

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3. (Original post by Haza100)
Hello!

I was working on these questions yesterday:

https://www.dropbox.com/sh/x2qs0oe7a...IdhTgfx2a?dl=0

I don't understand why in (3a), the numerator cancels to . Can someone explain this to me?

Can you see how to finish this off?
4. (Original post by drandy76)
When you expand the brackets you should and simplify, you should get r2^r+1-r2^r, have you gotten to that stage?

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Only just realised that . Duh! Guess I worked for too long yesterday haha.
5. (Original post by Zacken)

Can you see how to finish this off?
Yeah thanks, I stupidly missed . Thanks
6. (Original post by Haza100)

Also, I don't understand the method the mark scheme uses to prove that (4b) is true, I would have expanded the summation of a^3 + b^3 + y^3 and equated it with 3aby but this would have taken ages for a 3 mark question. Can someone explain the intermediate steps in the mark scheme answer?
So you know that a, b, c are roots of the equation (I'm using those in place of and respectively)

So you know that:

You can now add all three equations together to get:

You've found already in the above parts, so plug that in. Can you now see how to finish off?
7. (Original post by Haza100)
Only just realised that . Duh! Guess I worked for too long yesterday haha.
For 4(b) it looks like they've done an equivalent to what you did, but used summation formulas for conciseness

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8. (Original post by Zacken)
So you know that a, b, c are roots of the equation (I'm using those in place of and respectively)

So you know that:

You can now add all three equations together to get:

You've found already in the above parts, so plug that in. Can you now see how to finish off?
Ah yes, thank you so much.
9. (Original post by Haza100)
Ah yes, thank you so much.
10. am I too late?

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Updated: February 29, 2016
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