Simultaneous equation problem

Tskadem

Hey, really stuck on this one
xy=56/(x-y)
x^2+y^2=113/(x-y)

Reply 1

Chlorophile

Original post by Tskadem

Hey, really stuck on this one
xy=56/(x-y)
x^2+y^2=113/(x-y)

Are you sure that's 113 and not 112?

Reply 2

Tskadem

Nope, Diego 113

Posted from TSR Mobile

Reply 3

Tskadem

*defo

Posted from TSR Mobile

Reply 4

Gaiaphage

I think that's a typo in your textbook/whatever, it should be 112. Then you'd just do 2xy=x^2+y^2

Reply 5

Jammy Duel

Think about it, you get 2xy=x^2+y^2=>x^2-2xy+y^2=0=>(x-y)^2=0=>x=y.
Then plug that into the denominators and you get division by 0

Reply 6

Chlorophile

derp

(edited 9 years ago)

Reply 7

Jammy Duel

Original post by Chlorophile

I keep getting nonsensical answers from this question too. I don't think it has any solutions.

With 113 it should have solutions, just not very nice ones, ill get some paper in a minute.

Reply 8

Chlorophile

Original post by Jammy Duel

With 113 it should have solutions, just not very nice ones, ill get some paper in a minute.

I put this into an online equation solver and it actually does have very nice integer solutions. No idea how it got to them though.

Reply 9

Jammy Duel

Original post by Chlorophile

I put this into an online equation solver and it actually does have very nice integer solutions. No idea how it got to them though.

I think I know how to, I just can't remember it.

Reply 10

Jammy Duel

Looking up the solutions it seems to be obvious where they come from, so I guess work backwards.
Working forwards, not that it's necessarily helpful, I have a cubic: x^3-y^3=169.
In theory from that point you could trial and error the solutions, depending on wording of the question (if it came up in an exam) you could get away with that.

(edited 9 years ago)

Reply 11

Chlorophile

Original post by Jammy Duel

There must be a better way of doing it though. I've come up with dozens of different forms of the equation, none of them directly lead to an obvious answer.

Reply 12

Jammy Duel

Original post by Chlorophile

There must be a better way of doing it though. I've come up with dozens of different forms of the equation, none of them directly lead to an obvious answer.

Well, again from knowing the solutions somewhat, there is always the spotting it from the off, which is in hindsight glaringly obvious.

Reply 13

Chlorophile

Original post by Jammy Duel

Well, again from knowing the solutions somewhat, there is always the spotting it from the off, which is in hindsight glaringly obvious.

It's not that glaringly obvious. 56 appears in quite a few of the equations I came up with but so do lots of other numbers like 169, 225, 2root14, etc.

Reply 14

Jammy Duel

Original post by Chlorophile

It's not that glaringly obvious. 56 appears in quite a few of the equations I came up with but so do lots of other numbers like 169, 225, 2root14, etc.

Well given that it doesn't seem possible, or at least easy, to isolate either variable that it's a case of forming one of the correct set of equations, obviously trivial to solve rather than a cubic, and my line has been trying to get to that family of equations, or one of the families that would work.

Reply 15

pzoDe

Notice that after multiplying both equations by

x-y

the second equation can be written in terms of the first equation by manipulating the values on the RHS.

For the full solution, view the spoiler below.

Spoiler