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VERY HARD further maths question

Let a,b and c be real numbers such that a+b+c=0 and let
(1+ax)(1+bx)(1+cx)=1+qx^2+rx^3
for all real x.Show that q=bc+ca++ab and r=abc

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Reply 1
Avatar for B_9710
B_9710
18
Expand out and equate coefficients.
Original post by B_9710
Expand out and equate coefficients.


Not going to work
Original post by STRANGER2
Not going to work


A shame, because it does :tongue:
Original post by STRANGER2
Not going to work


Yes it does. And it's not even close to being a 'VERY HARD' question.
Peasy.. As above.
If you couldn't do that..
Reply 6
Avatar for M14B
M14B
18
I thought it was hard.
:redface:
Let's carry on with the question then: (I'm mad!)

Show that the coefficient of x^n in the series expansion (in ascending powers of x) of ln(1+qx^2+rx^3) is (-1)^n+1 Sn where
Sn= (a^n+b^n+c^n)/n
where n>1

Btw if it's getting too tough for anyone it's ok this is only for top maths students
(If u get this question right I'll carry on because question not finished)
Original post by STRANGER2
Let's carry on with the question then: (I'm mad!)

Show that the coefficient of x^n in the series expansion (in ascending powers of x) of ln(1+qx^2+rx^3) is (-1)^n+1 Sn where
Sn= (a^n+b^n+c^n)/n
where n>1

Btw if it's getting too tough for anyone it's ok this is only for top maths students
(If u get this question right I'll carry on because question not finished)


what have you tried?
Getting @Zacken involved in this :P
Reply 10
Avatar for B_9710
B_9710
18
Original post by STRANGER2
Let's carry on with the question then: (I'm mad!)

Show that the coefficient of x^n in the series expansion (in ascending powers of x) of ln(1+qx^2+rx^3) is (-1)^n+1 Sn where
Sn= (a^n+b^n+c^n)/n
where n>1

Btw if it's getting too tough for anyone it's ok this is only for top maths students
(If u get this question right I'll carry on because question not finished)


Well we know the quadratic can be factorised as above so you get a product of linear expressions inside the log function. Using log laws you can add these separately quite easily as you should remember the expansion of ln⁡(1+x) \ln (1+x) .
I'm at GCSE level at the moment. I don't like the look of having to learn this... ;(
Original post by Tasty Apple
I'm at GCSE level at the moment. I don't like the look of having to learn this... ;(


It's not too bad really. You'll learn a simpler version at AS.
Reply 13
Avatar for Zacken
Zacken
22
Original post by STRANGER2
Let's carry on with the question then: (I'm mad!)

Show that the coefficient of x^n in the series expansion (in ascending powers of x) of ln(1+qx^2+rx^3) is (-1)^n+1 Sn where
Sn= (a^n+b^n+c^n)/n
where n>1

Btw if it's getting too tough for anyone it's ok this is only for top maths students
(If u get this question right I'll carry on because question not finished)


I'm fairly sure you've just gotten this from a STEP question, in which case - work it out yourself instead of having people do it for you.
Original post by B_9710
Well we know the quadratic can be factorised as above so you get a product of linear expressions inside the log function. Using log laws you can add these separately quite easily as you should remember the expansion of ln⁡(1+x) \ln (1+x) .


Give me a worked solution or just quit and tell me you're not top maths student
if u do that I'll work it out for u
Original post by morgan8002
It's not too bad really. You'll learn a simpler version at AS.


You sure? Because there's a lot of letters there. And what does ^ mean?

Actually, don't tell me. I don't think I want to know...
Original post by Tasty Apple
You sure? Because there's a lot of letters there. And what does ^ mean?

Actually, don't tell me. I don't think I want to know...


It just means 'to the power of'
Original post by Tasty Apple
I'm at GCSE level at the moment. I don't like the look of having to learn this... ;(


Things often look difficult until you've studied them and practiced a fair amount. You might come across the first part in A-level maths and the second part in Further Maths.
Original post by Tasty Apple
You sure? Because there's a lot of letters there. And what does ^ mean?

Actually, don't tell me. I don't think I want to know...


It's just a shorthand for power because you can't write superscripts easily on a keyboard. x^n = xnx^n.
Original post by morgan8002
It's just a shorthand for power because you can't write superscripts easily on a keyboard. x^n = xnx^n.


Btw I made another thread called difficult logarithms question if anyone think that he is very good at maths go ahead and have a look at it

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