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any thoughts/ideas?

couldn't u find a longer eq? :P

its a monstrous beast...

:P

I think it is smth like (ax-by)^3 bu i can't tell wht r a and b

but*

(x-2*y)*(2*x-1+3*y)*(2*x-5+3*y)

(x-2y)(2x+3y-5)(2x+3y-1)=0

i'm not planning to deal with this..u do it...:P

i got it first, please medal

u rock cantorset! but we cant use comps!

how do you know i use computer

:)

@contorset: lol, its obvious. :P

hey how did u do tht?

well witout at computer its LUCK..

I didn't do it on my own, wolframalpha

maple

and how do u do it in comp?

haha... if u had a good luck u wud put x=2y and inspect!!!

you can do it in wolframalpha,

then u get (x-2y) and get others by dividing

i should not give out my secrets though

k. but tat doesnt solve the problem..

x=2y ? you mean substitute

yes...

but see tat doesnt..solve the problem

we have to find positive integer solutions..

woww

but you can pick anything, x = 4y for instance

and i thought u guys were smart :P:P:P

i dont see any logic in this problem

ya cantorset that's truly possible but as i said we need luck and brain-breaking insights...

see..now how to find the solution?

for the first one(x-2y),
x = 2I
y=I

yes

what for 2x+3y-5=0

its obvious (1,1) but are there others..THIS IS DIOPHANTINE!!

OK lets see, x + 3y/2 =5/2
x=(5-3y)/2
5-3y should be even,

so y is odd.

what about 2x+3y=1? yay...theres no positive integers here in this equation..so this is infertile:P

Why do you think so?

how can u get postive integers (x,y) from 2x+3y<5

there are none...:P

infertile..mother has no babies:P

that can be solved with euclids algorithm

Oh sorry, i dint read that 'positive' part! :P

this mother 2x+3y=5 has only one baby i.e. (1,1)

So our answer: (1,1) and (2n,n)

So its done, (n,2n) U (1,1)

Openstudy rocks!! thnx evrybody!

Oops (2n,n).
yes right

Going to deal with literature bye and have a good time :)

, amog, you wrote x= 1, y = 21?

@angela: buh-bye.
@cantorset: It was an 'I' (eye)

for the first one(x-2y), x = 2I y=I

Yes i corrected it, didn't I?

hi cantorset...do u mind givin me an idea how to have a factor to the eqn..

suppose i have the baddest luck and go on inspecting from x=3y;x=4y....

wait, ... start over . why would i think to use x = 3y or anything like that

also its 3 linear, not a conic

or worser x=3y+7 etc..

yeah

you mean because the solution is ( ax + by ) ( dx + cy + ...

and so we start checking by x=y;x=2y;x=3y...

if the question does not mean to torment us we can get the factor in a few trials...

k..thnx evrybody for helping..:)

what do you mean by constant term in the equation

term with no variables attched..

oh right

the final solution is 3 linears, right?

yups...family of 3 straight line

cool, so ok , theres no constant term, and clearly, (0,0) works

yups..try looking for x=y,2y,3y,...here u need luck

so that tells us that x = ay or y = ax must be one of the solutions?

yes..true

but only for a=2

i.e.(2n,n)

right, but thats only if you do the long division< right?

if you know to assume, 2x = y ?

or wait, you know that (0,0) is a solution and (1,1) is a solution, right>

yes...not assume but see if its correct by replacing 2x by y OR replacing y by 2x

(1,1) is known after we get other factors using x-2y

hmmm, yes but i mean is there something that would make us want to to do x = 2y

oh ,

tat is LUCK!

( 1,-1) is another solution then

4x^2 + 9y^2 + 12xy -2x -15y +5 =0
How do you solve this btw?

from discriminant criteria for various conics see if its parabola/ellipse/hyperbola..

OK!

amogh u indian?

So here its a parabola

tats what wolframalpha says...

I didn't use wolframalpha for it? Afterall we in India are not allowed to use any calc! :P

And I like it!

in which class r u?

Just went into XII

wer r u frm?

kolkata passed 12

what are the possible shapes of a third degree x,y equation, a conic is second degree,

Cool, did you give the JEE?

may be:
1.family of straight lines..
2. a strt line and a conic

gave it! but didnt get it:(

hope u get:)

Thanks :) So what plans?

very cool saubhik, didnt know that

dont know ....awaiting for AIEEE and WBJEE and ISI results...

whats AIEEE?

All India Engineering Entrance Examination (in india)

thnx..cantorset...

All the best buddy!

saubhik, i got a problem for ya

mayb ei should post new one

yups...

post new one..