Question

Something I forgot in quadratics, need a reminder

Answer 1

\[\alpha^2 + \beta^2=?\]

Answer 2

α^2+β^2= ( α+β)^2 - 2αβ

Answer 3

thanks :)

Answer 4

Just a formula, my luck to earn points :)

Answer 5

lol

Answer 6

Btw, do you know that this is a symmetric function?

Answer 7

what do u mean by symmetric functions... don't know what that is or means lol :P you wanna explain that to me :)

Answer 8

plot the function on a paper, find the vertex fold the paper about the the straight line passing through the vertex.

Answer 9

A function of \( \alpha\) and \(\beta \) is said to be symmetric if it remains unchanged when \( \alpha\) and \(\beta \) are interchanged.

Answer 10

and addition is commutative, hence \(\alpha + \beta \) is symmetric... makes sense

Answer 11

Exercise: What is the symmetric function for \( α^5+β^5 \)

Answer 12

that looks odd with the exponents being 5 but i'm gonna go ahead and say
\(\alpha^5 + \beta^5=(\alpha + \beta)^5-5\alpha \beta \) :P idk if that's right lol :P

Answer 13

For Ishaan or the silent Turing, What is the symmetric function for \( |α+β| \)

Answer 14

btw that's not right saso.

Answer 15

i figured, it was random thought, not mathematically arrived. i should give it a thought

Answer 16

I don't think I see how this works
I was thinking a^5+b^5=(a+b)^5-(all that expansion stuff) for the other one

Answer 17

...but I'm only just now learning what a symmetric function is

Answer 18

wait, i thought u factor out the exponent if the base is the same...? didn't think about it this way...

Answer 19

wiat..... ohhh you add the exponents if the bases are the same and factor out the exponents if it's the same on both terms.... sigh

Answer 20

how about...\[|a+b|=\sqrt{a^2+2ab+b^2}\]...
yeah I don't know what I'm doing lol

Answer 21

isn't it weird how i attempt ffm's challenges yet i seem to have issues with some basic stuff...? :@@@@

Answer 22

I've never gotten one of fools challenges, and I don't think I'll do particularly well at 2:00am, so goodnight y'all!

Answer 23

ttyl :)

Answer 24

Symmetric function are usually writing in terms of (a+b) and/or (a-b) and/or ab

Answer 25

I only know about quadratic functions, and I think all quadratic functions are symmetric.

I don't get what you mean by \(|\alpha + \beta|\)? Are \(\alpha\) and \(\beta\) roots of a quadratic function?

Answer 26

Ishaan are u in uni?

Answer 27

No, why do you ask?
I am just lowly High School graduate.

Answer 28

you seem smarter than hs level, the only thing i can think of u being is a college student :/ oh well, what uni/colleges are u applying/applied to?

Answer 29

Okay, so I read your (FoolForMath) definition again, "A function of α and β is said to be symmetric if it remains unchanged when α and β are interchanged".

I think any function which could be arranged in the form of \((x-\alpha_1)(x-\alpha_2)\ldots(x-\alpha_{n})\) is symmetric.
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Honestly saso I am not smart, I am an idiot. If I were smart I'd be in IIT (Indian Institute of Technology) but since I am idiot I end up wasting a lot of time (Procrastination). I am only applying to Colleges and Universities in my country.

Answer 30

FoolForMath by symmetric function for \(\alpha^5 + \beta^5\), what do you imply? Do you mean a function whose roots are \(\alpha^5\) and \(\beta^5\)?

Answer 31

Ishaan, for finding the symmetric function expand \( (\alpha + \beta)^5 \) and then arrange, note the final answer would only have \( (\alpha + \beta) \) and \( (\alpha \times \beta) \) in the RHS.

Answer 32

FoolForMath but what are \(\alpha^5\) and \(\beta^5\)? Are they roots of a quadratic function? I am confused :-/

Answer 33

\(\alpha\) and \(\beta\) are the roots of quadratic polynomial.

Answer 34

So when you say, find a symmetric function for \(\alpha^5\) and \(\beta^5\). What do you mean?

Answer 35

Correction. \[\alpha^5 + \beta^5\]