What's new
Fantasy Football - Footballguys Forums

This is a sample guest message. Register a free account today to become a member! Once signed in, you'll be able to participate on this site by adding your own topics and posts, as well as connect with other members through your own private inbox!

tricky algebra problem (1 Viewer)

Maurile Tremblay

Maurile Tremblay

Administrator
Staff member
a/(b+c) + b/(a+c) + c/(a+b) = 4

Find a solution where a, b, and c are all positive integers.

I played around with this for about 30-60 minutes (I didn't keep track) before giving up and looking at the answer. I don't think it was a waste of time. The explanation (linked below) is very good, which is why I'm posting this. It's better if, before reading it, you work on the problem long enough to convince yourself that you're not going to solve it within a reasonable amount of time (unless your math knowledge is pretty darn esoteric).

Answer: https://www.quora.com/How-do-you-find-the-integer-solutions-to-frac-x-y+z-+-frac-y-z+x-+-frac-z-x+y-4

 
Last edited by a moderator:
Maurile Tremblay said:
a/(b+c) + b/(a+c) + c/(a+b) = 4

Find a solution where a, b, and c are all positive integers.

I played around with this for about 30 minutes before giving up and looking at the answer. I don't think it was a waste of time. The explanation (linked below) is very good, which is why I'm posting this. It's better if, before reading it, you work on the problem long enough to convince yourself that you're not going to solve it within a reasonable amount of time (unless your math knowledge is pretty darn esoteric).

Answer: https://www.quora.com/How-do-you-find-the-integer-solutions-to-frac-x-y+z-+-frac-y-z+x-+-frac-z-x+y-4
Click to expand...
Played around for 5 minutes and closest I could get was 23, 3, 3 but it came out to 4.06

 
Don't Noonan said:
Played around for 5 minutes and closest I could get was 23, 3, 3 but it came out to 4.06
Click to expand...
1, 7, 30 gets to 4.00283 -- so close in value, and yet conceptually still a zillion miles away. Denominators of 37, 31, and 8 are not going to allow summing to an integer.

 
Last edited by a moderator:
Closest I can get is 

a3 + b3 + c3 - 3(a2b + a2c + b2a + b2c + c2a + c2b) - 5abc = 0

Not helping me at all  :loco:

 
Last edited by a moderator:
Dickies said:
Closest I can get is 

a3 + b3 + c3 - 3(a2b + a2c + b2a + b2c + c2a + c2b) - 5abc = 0

Not helping me at all  :loco:
Click to expand...
Right. I got to that point and then decided, "I can't actually solve this algebraically. I'm going to just start putting numbers into Excel..." After doing that for a while, I conceptually proved to myself that there's no way b or c could be less than 100 (starting with a=1), and that's when I looked at the explanation.

 
Maurile Tremblay said:
a/(b+c) + b/(a+c) + c/(a+b) = 4

Find a solution where a, b, and c are all positive integers.

I played around with this for about 30-60 minutes (I didn't keep track) before giving up and looking at the answer. I don't think it was a waste of time. The explanation (linked below) is very good, which is why I'm posting this. It's better if, before reading it, you work on the problem long enough to convince yourself that you're not going to solve it within a reasonable amount of time (unless your math knowledge is pretty darn esoteric).

Answer: https://www.quora.com/How-do-you-find-the-integer-solutions-to-frac-x-y+z-+-frac-y-z+x-+-frac-z-x+y-4
Click to expand...
One solution.

 
Maurile Tremblay said:
Right. I got to that point and then decided, "I can't actually solve this algebraically. I'm going to just start putting numbers into Excel..." After doing that for a while, I conceptually proved to myself that there's no way b or c could be less than 100 (starting with a=1), and that's when I looked at the explanation.
Click to expand...
Got here too, started scrolling down the thread, haven't looked at the solution yet.  Dang....

 
Maurile Tremblay said:
Right. I got to that point and then decided, "I can't actually solve this algebraically. I'm going to just start putting numbers into Excel..." After doing that for a while, I conceptually proved to myself that there's no way b or c could be less than 100 (starting with a=1), and that's when I looked at the explanation.
Click to expand...
Me too.  And then when I read the explanation, I remembered why I didn't like higher math.  Once things got too abstract I lost interest.  There's only so many puzzles one can do for the sake of doing puzzles.  At least, this one. :)   But God bless the theoretical mathematicians, where would we be without them?

 
Maurile Tremblay said:
a/(b+c) + b/(a+c) + c/(a+b) = 4

Find a solution where a, b, and c are all positive integers.

I played around with this for about 30-60 minutes (I didn't keep track) before giving up and looking at the answer. I don't think it was a waste of time. The explanation (linked below) is very good, which is why I'm posting this. It's better if, before reading it, you work on the problem long enough to convince yourself that you're not going to solve it within a reasonable amount of time (unless your math knowledge is pretty darn esoteric).

Answer: https://www.quora.com/How-do-you-find-the-integer-solutions-to-frac-x-y+z-+-frac-y-z+x-+-frac-z-x+y-4
Click to expand...
Took me 15 seconds on Google 

 
Gopher State said:
Maurile Tremblay said:
a/(b+c) + b/(a+c) + c/(a+b) = 4

Find a solution where a, b, and c are all positive integers.

I played around with this for about 30-60 minutes (I didn't keep track) before giving up and looking at the answer. I don't think it was a waste of time. The explanation (linked below) is very good, which is why I'm posting this. It's better if, before reading it, you work on the problem long enough to convince yourself that you're not going to solve it within a reasonable amount of time (unless your math knowledge is pretty darn esoteric).

Answer: https://www.quora.com/How-do-you-find-the-integer-solutions-to-frac-x-y+z-+-frac-y-z+x-+-frac-z-x+y-4
Click to expand...
Took me 15 seconds on Google 
Click to expand...
Well that's a complete waste of 15 seconds you'll never get back.

I GAVE YOU THE LINK!!

 
Just read the answer after giving up.  Guy does a good job of explaining the answer, but I still don't really grasp it. 

 
You'd think that I'd feel better about myself after spending 15 minutes on this and then looking at the answer. But no.

 
Dickies said:
Just read the answer after giving up.  Guy does a good job of explaining the answer, but I still don't really grasp it. 
Click to expand...
There are very few people in the world who "really" grasp. It wouldn't surprise me if MT was one of them, but for the most part, we are all pretty dumb.

 
I was going to write a bit of optimization code to find the answer, but I am glad I read the answer first. I don't think it would have worked. I am not sure it would ever try such large numbers.I am pretty sure I would have found a local minima.

 
I haven't looked at the answer yet or anything outside of the 1st post.

First kept trying 1,2, and a different #'s then multiples  and finally tried 1 twice and finally figure out that way.

7,1,1

Never mind I'm dumb :(

 
Last edited by a moderator:
You must log in or register to reply here.

Similar threads

John Maddens Lunchbox
Desert Island Song Draft - Alphabet thievery afoot - Thievery abounds, XTC and Queen popular. Starting Round 25. Chaos coming
37 38 39
Replies
2K
Views
50K
northern exposure
northern exposure
GordonGekko
What Is The Worst Part Of Your Main Job/Career That No One Ever Told You About? (2/30)
Replies
23
Views
1K
MTskibum
MTskibum
Raybenz19
Here is Practical Explanation about Next Life, Purpose of Human Life, philosophical/religious facts, theories etc.
2
Replies
87
Views
4K
3C's
3C's

Users who are viewing this thread

Total: 1 (members: 0, guests: 1)
Back
Top