No known formula ??? (1 Viewer)

[abdooooo!!!]

Originally posted by freaking_out
don't worry if ur confused- that can happen when ur trying to read/type maths ova the net using funny symbols. LoL

yeah the only reason i can think of is that the dude infact misquoted patel.

im taking his statement as meaning that expressing it like this: a^2 + b^2 + c^2 = (a + b + c)^2 - 2(ab + ac + bc) is a general formula you normally remember to use to do the question. and when it is power of 4 it can be derived long hand, but its just not known as a formula that you would normally use as it is way too long to even write out compared to the rather simple substitution method that can be used to solve the question.

anyways its a bit too late for me... me need bed now... me hate school.

 

[freaking_out]

gnite abdoo!

 

[CrashOveride]

Originally posted by KeypadSDM
I probably got it wrong. I'll type it up in the morning. I'm going to sleep.

But I'll explain the statement:

" there is no known formula that relates (summation)@^4 with (summation)@ "

This means, there is no formula where:

A⁴ + B⁴ + C⁴ + ... + n⁴ = f(A + B + C + ... n)

But there is a formula where there are multiple functions on the right hand side, in the form:

f(A + B + C + ... n)
g(AB + BC + CD + ... nA)
h(ABC + BCD + CDE + ... nAB)
etc.

Yeah, that's quite right. I think i automatically assumed he (Patel....and no i didnt misquote anything) was talking about summation in terms of "two at a time, three at a time", as implied by your statement.

On closer inspection people, no ground breaking discovery!

I realised my sneaky friend just tore off patel's (simple) substitution method but converted it by way into a formula.

To say no more, here is what i was talking about:
let roots be X, Y , Z

for ax^3 + bx^2 + cx + d = 0:
(summation)X^4 = -b[(summation)X^3) - c[(summation)X^2] -d[(summation)X]

this does give the right answer...but as i just noticed its just a more quantitative interpretation of patel's method. Sorry for the "false alarm"

 

[KeypadSDM]

Originally posted by abdooooo!!!
what are you saying?? shortcut? if you do it the relationship way its the longest cut you can get... but the statement of patel is ultmately flawed... unless he is talking about something else instead of polynomial roots and their relationship.

at first i thought the statement meant in the form of sum[a], sum[ab] and sum[abc]... but then keypad started talking about only sum[a] then im confused... now i've re-read the statement it just does not make sence anymore.

Ok, I think alot of people don't know what Sum[A] means.

Sum[A] refers to the sum of roots in the polynomial
Sum[AB] refers to the sum of roots in pairs.
etc.

 

[freaking_out]

Originally posted by KeypadSDM
Ok, I think alot of people don't know what Sum[A] means.

Sum[A] refers to the sum of roots in the polynomial
Sum[AB] refers to the sum of roots in pairs.
etc.

yeah, and in most books, the "sum" bit is represented by this funny "E" looking sign. i forget what its called.

 

[CrashOveride]

Sigma, I believe.

 

[Xayma]

Originally posted by CrashOveride
Sigma, I believe.

Yep it is capital (I think) sigma meaning "Sum of"

 

[freaking_out]

Originally posted by CrashOveride
Sigma, I believe.

yeah, thats what its called- man my brain has gone dead after the hsc, beginning to forget many things.

 

[KeypadSDM]

Maybe we should invent some more notation?

http://www.boredofstudies.org/community/showthread.php?s=&threadid=7127&perpage=15&pagenumber=2

 

[Grey Council]

uh, thats in the fitzpatrick book, i think.

But thats how our teacher taught us 3u polynomials. The heck, i just skimmed over what you posted originally, then had a go at Abdoooo. lol

but isn't that kinda a theory for polynomials? hmmm, i'm confused. Just like abdoooo. But abdooo's always confused, so thats okay.

lol @ abdoooo

 

[abdooooo!!!]

Originally posted by Grey Council
uh, thats in the fitzpatrick book, i think.

But thats how our teacher taught us 3u polynomials. The heck, i just skimmed over what you posted originally, then had a go at Abdoooo. lol

but isn't that kinda a theory for polynomials? hmmm, i'm confused. Just like abdoooo. But abdooo's always confused, so thats okay.

lol @ abdoooo

yea hobbit lover... you can talk...
grey council guardian idiot.

what did i ever do to you??? i hate you!!!

Originally posted by CrashOveride
Yeah, that's quite right. I think i automatically assumed he (Patel....and no i didnt misquote anything) was talking about summation in terms of "two at a time, three at a time", as implied by your statement.

you sure you didn't misquote patel. im not having a go at you or anything but are you sure that the statement is absutely correct.

when i learnt polynomials for solving that question i was taught that there are normally 2 methods you proceed.

the first is just substuting it, the roots back into the equation and add them together to get the sum, like what patel did.

the second is converting the (sum)a^n in terms of (sum)a, (sum)ab, (sum)abc... etc.

but with your patel's statement, it simply says in terms of "just" sum(a). not including any other sum that is a root relationship that can be used to solve the problem at hand.

my question is what does that statement have to do with the question? its either wrong (should be like my way) or it is non related to the question you are trying to solve.

 

[CrashOveride]

Once again, i did not misquote anything. Its quoted verbatum.

He said in terms of sum(a)...and his statement is correct. You could do it your way also but with sum(a) sum(ab) and so on it gets very long-winded. If you refer to the formula i put up earlier, it doesnt deal with any ab's or abc's but it works with powers....and as u see Patel said only sum of the roots..nothing about powers....so he is in fact correct.

Refer to posts of KeyPad also. He seems to know what he's talking about

I was quick to post this originally because my friend was claiming to write into the local newspaper (loser) ....ok maybe just e-mail Patel or something and yeah....and our teacher was like just blank the whole lesson [seems the further we go on with 4u the less stable his memory becomes]

[/rant]

 

[abdooooo!!!]

statement: "there is no known formula that relates (summation)@^4 with (summation)@ "

what does that have to do with solving a^4 + b^4 + c^4? you get what i am saying? so what if you can't express it like that? who the hell express it like that to solve the problem you're doing? its either wrong (should be like (sum)a, (sum)ab, (sum)abc) or its totally non-related to solving a^4 + b^4 + c^4.

as i said there are two ways: the substution method which your friend or you claimed to be disproving the statement:

"for ax^3 + bx^2 + cx + d = 0:
(summation)X^4 = -b[(summation)X^3) - c[(summation)X^2] -d[(summation)X]. "
as you can see its expressed in terms of "powers" of (sum)a and not "just" (sum)a^1 (the one is there to say that no powers lol). this is just the substution method that has been invented long ago.

and there is the relationship way, which is expressing it in terms of (sum)a, (sum)ab, (sum)abc... which i think is what patel is trying to say based on my understanding of that question. who else has that book??? someone check the statement for me...

edit: if you still don't get my arguement, look at this: can a^2 + b^2 + c^2 be expressed in terms "just" (sum)a??? i mean nothing can, no matter what their power is... i would find it strange that patel would say such a thing as in only (sum)a^"4" cannot be expressed in (sum)a... the fact is no matter what the power is unless its 1 then none of them can. then what is the statement for??? its either non-related or wrong... thats my arguement.

 

[CrashOveride]

I will state for the final time, it IS related to the question (patel says that then he does sub method), it is not a misquote and Patel says it exactly like that.

"what does that have to do with solving a^4 + b^4 + c^4? you get what i am saying? so what if you can't express it like that?"

I was NOT arguing the point that it HAD to be solved like that. I was merely rasing discussion because, as you have pointed out now, why would Patel say that ?

"as you can see its expressed in terms of "powers" of (sum)a and not "just" (sum)a^1 (the one is there to say that no powers lol). this is just the substution method that has been invented long ago.
"

Yes, i just said that before.

"and there is the relationship way, which is expressing it in terms of (sum)a, (sum)ab, (sum)abc... which i think is what patel is trying to say based on my understanding of that question"

Perhaps he is "meaning" this. Unfortunately, i cannot read between the lines and pick up on what he is "meaning", im going soley with what he wrote.

"as i said there are two ways: the substution method which your friend or you claimed to be disproving the statement:

"for ax^3 + bx^2 + cx + d = 0:
(summation)X^4 = -b[(summation)X^3) - c[(summation)X^2] -d[(summation)X]. ""

I was not disproving that. I posted that, which can be seen as a type of "formula interpretation" of the substitution method.

 

[abdooooo!!!]

ok ok. i think we understand each other now with all the weird symbols... so patel can't write books properly.

what kind of gay confusing statement is that??? it doesn't even make sense in the context of what he is talking about... ahahaha.