I don't get any ideas after seeing this problem.

[round lion]

I would appreciate it if anyone could tell me how to attempt questions like these. What ideas are common. Where can i learn more about systems of equations like these. (I can't bother with brainless jumping of variables here and there. Help).

[heady owl]

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[round lion]

@reef wind @whole pike @gusty parrot @junior agate @haughty lily

[whole pike]

Excuse me?

[round lion]

Can you help?

[whole pike]

We don’t ping everyone in the server to get help, we post and wait for our helpers to come

Please don’t do this again

[round lion]

I tagged people who wont mind getting tagged i think

[round lion]

Ok imma stop

[whole pike]

How can you know that?

[whole pike]

Thank you

[round lion]

I have some history with them perhaps

[reef wind]

im busy with ioi prep, ioi next week

[round lion]

No worries mate. All the best for ioi😄

[knotty fable]

Agamjeet mocks??

[round lion]

Yeah

[lilac grove]

Maybe try making polynomial equations

You can also try finding all the cases for the equations and keep on substituting until you find b+d

But its gonna be lengthy

Like for eg ce=72

The possible values for c and e would be the factors of 72

And then you apply all the cases in another equation of which consist of c and e

But the shi- is too lengthy

[junior agate]

in this case you can happen to see that this is a convolution of <1,a,b,c> and <1,d,e> and turn this into a polynomial phrasing, yes, but i don’t think i’ve ever seen this, it’s not a common idea i’d say

[lilac grove]

True

But its like you have no choice

[lilac grove]

Like this thing will eventually reduces the possibility of the values of them

But goofy ah process

Too lazy yk

There's must be some other wat

Way

[round lion]

Well you are on some strangely correct path. They did use (1+a+b+c)(1+d+e) and then they turned it into poly

[lilac grove]

where is this question from?

[lilac grove]

that should work

but that cant be the only way

[round lion]

SMT 2018

[lilac grove]

i see

[round lion]

Yeah, bashing with cases may as well work

[lilac grove]

yeah but like you would get an answer

but dont do it

cuz it would waste a lot of time

if you are preparing for some test

[round lion]

And perhaps a crazy repeated substitution would work giving us a cubic in the end. Then apply the 2 page long formula and done

[round lion]

Yeah i wont

[lilac grove]

😭

ill see if i can figure out something else

[round lion]

Can you tell me the name of the method they used, imma send in the sol

[round lion]

Is that ok for you?

[lilac grove]

substituting?

[lilac grove]

which one

[round lion]

What g=gen was talking about

[lilac grove]

i dont think its a specific method

its all based on observations

[round lion]

Ohh

[round lion]

You wanna see the sol ?

[lilac grove]

yeah please

[round lion]

Official one

[lilac grove]

yep

[lilac grove]

aight cool

this is literally just manipulating

[round lion]

Why does the end step work though

[round lion]

Experience dependent problem

[lilac grove]

those 3 equations?

he has just arranged this into different ways

basically first you do the brakets like they said there and then match each term with a power of x

brackets*

then the polynomial we will get aligns with the terms we have

so we can substitute values

and then just factorize

and arrange it again in the first form

and then the guy just has expressed it in 3 ways

[round lion]

Ohh okh

[round lion]

Thanks

[keen tundra]

@round lion has given 1 rep to @lilac grove

[junior agate]

strangely correct? lol

[round lion]

😂 haha

[junior agate]

as for common strategies on systems of equations:

• id say the most common is to not try to find the variables just whatever exactly the question asks for (doesn’t apply here)
• linearly combine things to eliminate
• vieta’s formulas are really common (symmetric polynomials)
• if asked for integer solutions you can consider taking the equations modulo p
• if you see an expression showing up repeatedly consider declaring it as a variable
• if there are more variables than equations (underspecified) it may be an inequality (toy example is x^2 + y^2 = 0) or the thing they ask for is specified while some other variables aren’t (toy example is x + y + z = 0, y + z = 1, find x)
  in both cases a way you can do this is pick some variable and set it to a convenient thing, probably -1, 0, 1, 2
  in the former case, the remaining system will probably have no solution and in the latter, you’ll get the same final answer for any choice
• generally looking for patterns is how i found the convolution solution for this one
• know how to factor 1 var and probably 2+ variable polynomials
• ideally the goal of math competition problems is to make you figure things out that you’ve never seen, more than to memorize a bunch of tricks, so learn to think creatively which is a skill you build over time

[round lion]

Thanks mate 😄.

[keen tundra]

@round lion has given 1 rep to @junior agate

[round lion]

+close