I want to get every solution possible, any method besides trying random values?
#How to solve?
median rose
trim heathBOT
shrewd cargo
Hint: Assuming $x\cdot y \ne 0 \implies \frac 9 x + \frac 4 y = 1$
fallow valeBOT
HitenTandon
outer phoenix
I want to get every solution possible, any method besides trying random values?
What is this for? I live to know anything about science and math
median rose
What is this for? I live to know anything about science and math
it was from another problem but i adapted
so ig you can say its just for doing math sake
outer phoenix
If its not much of a problem could you explain to me how it works?
median rose
trying to find all possible values of x and y, both of them being positive integers
outer phoenix
Ah i kinda get it, btw i saw you play chess?
median rose
yeah i do, just kinda rusty
outer phoenix
Oh i dont mind that at all i dont know anything about chess but love to learn it, i only play checkers
Do you may want to be friends and somehow play chess someday?
median rose
sure, pm me though cuz we are getting off topic 🫠
outer phoenix
Ty!!
median rose
Hint: Assuming $x\cdot y \ne 0 \implies \frac 9 x + \frac 4 y = 1$
still idk what to do after
umbral storm
If you isolate any of the variables, you get:
x = 9 + 36/(y-4)
You'll get a similar equation for y.
Since x and y are N, then 36/(y-4) must be an integer.
From this, we obtain that 0<(y-4)<=36
You'll get a similar equation for y, as well as another range for x.
Then, 36 is divisible by y-4.
So, y-4 can only be one of the divisors of 36.
$y-4={2^03^0, 2^13^0,...2^23^2}={1,2,3...36}$
fallow valeBOT
Adler
umbral storm
Of those 9, we now need to eliminate those that are not in the ranges we obtained before.
median rose
If you isolate any of the variables, you get:
x = 9 + 36/(y-4)
You'll get a simi...
It all makes sense now, thanks
median rose
$y-4={2^03^0, 2^13^0,...2^23^2}={1,2,3...36}$
just dont understand this last line
umbral storm
just dont understand this last line
It's a way to find all the divisors.
The prime factorization of 36 is 2^2 * 3^2.
So its divisors are all the combinations of those exponents and their lower values.
I hope a table helps
Mistake
1*1=1
umbral storm
ah its 2⁰*3⁰...?
yes
tardy fox
You can do:
-9y -4x + xy + 36 = 36
So : (x - 9) (y-4) = 36.
With this you can find every solution just by knowing that 1x36, 2x18, 3x12, 4x9, 6x6 and vice-versa are all equal to 36. This means that (x-9) is equal to (10-9) when (y-4) is 36 and so on. With this you can find all possible solutions :)
median rose
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