Technique behind solving 4 = $frac{a}{b+c} + frac{b}{a+c} + frac{c}{a+b}$












2














The question:



4 = $frac{a}{b+c} + frac{b}{a+c} + frac{c}{a+b}$



Where I have to find the minimum values for a, b and c and they have to be positive and whole?



I'm slightly confused by all the requests so it's a little tough to figure out the quirks. A step in the right direction would be great.










share|cite|improve this question


















  • 5




    What are trying to minimize? Is it $a + b + c$?
    – Alex Vong
    Nov 28 '18 at 4:42






  • 4




    Follow the following link:. google.co.in/url?sa=t&source=web&rct=j&url=http://…
    – RABI KUMAR CHAKRABORTY
    Nov 28 '18 at 5:13






  • 5




    According to this MO post, the smallest positive solution is $$smallbegin{align} a &= 4373612677928697257861252602371390152816537558161613618621437993378423467772036;\ b &= 36875131794129999827197811565225474825492979968971970996283137471637224634055579;\ c &= 154476802108746166441951315019919837485664325669565431700026634898253202035277999; end{align}$$ This is definitely not a algebra-precalculus/contest problem.
    – achille hui
    Nov 28 '18 at 9:56










  • Oh lol, so I've been bamboozled. Thanks for the answers though, it's interesting reading.
    – Mat Stornel
    Nov 28 '18 at 15:03
















2














The question:



4 = $frac{a}{b+c} + frac{b}{a+c} + frac{c}{a+b}$



Where I have to find the minimum values for a, b and c and they have to be positive and whole?



I'm slightly confused by all the requests so it's a little tough to figure out the quirks. A step in the right direction would be great.










share|cite|improve this question


















  • 5




    What are trying to minimize? Is it $a + b + c$?
    – Alex Vong
    Nov 28 '18 at 4:42






  • 4




    Follow the following link:. google.co.in/url?sa=t&source=web&rct=j&url=http://…
    – RABI KUMAR CHAKRABORTY
    Nov 28 '18 at 5:13






  • 5




    According to this MO post, the smallest positive solution is $$smallbegin{align} a &= 4373612677928697257861252602371390152816537558161613618621437993378423467772036;\ b &= 36875131794129999827197811565225474825492979968971970996283137471637224634055579;\ c &= 154476802108746166441951315019919837485664325669565431700026634898253202035277999; end{align}$$ This is definitely not a algebra-precalculus/contest problem.
    – achille hui
    Nov 28 '18 at 9:56










  • Oh lol, so I've been bamboozled. Thanks for the answers though, it's interesting reading.
    – Mat Stornel
    Nov 28 '18 at 15:03














2












2








2


4





The question:



4 = $frac{a}{b+c} + frac{b}{a+c} + frac{c}{a+b}$



Where I have to find the minimum values for a, b and c and they have to be positive and whole?



I'm slightly confused by all the requests so it's a little tough to figure out the quirks. A step in the right direction would be great.










share|cite|improve this question













The question:



4 = $frac{a}{b+c} + frac{b}{a+c} + frac{c}{a+b}$



Where I have to find the minimum values for a, b and c and they have to be positive and whole?



I'm slightly confused by all the requests so it's a little tough to figure out the quirks. A step in the right direction would be great.







algebra-precalculus contest-math algebraic-number-theory






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Nov 28 '18 at 4:37









Mat StornelMat Stornel

111




111








  • 5




    What are trying to minimize? Is it $a + b + c$?
    – Alex Vong
    Nov 28 '18 at 4:42






  • 4




    Follow the following link:. google.co.in/url?sa=t&source=web&rct=j&url=http://…
    – RABI KUMAR CHAKRABORTY
    Nov 28 '18 at 5:13






  • 5




    According to this MO post, the smallest positive solution is $$smallbegin{align} a &= 4373612677928697257861252602371390152816537558161613618621437993378423467772036;\ b &= 36875131794129999827197811565225474825492979968971970996283137471637224634055579;\ c &= 154476802108746166441951315019919837485664325669565431700026634898253202035277999; end{align}$$ This is definitely not a algebra-precalculus/contest problem.
    – achille hui
    Nov 28 '18 at 9:56










  • Oh lol, so I've been bamboozled. Thanks for the answers though, it's interesting reading.
    – Mat Stornel
    Nov 28 '18 at 15:03














  • 5




    What are trying to minimize? Is it $a + b + c$?
    – Alex Vong
    Nov 28 '18 at 4:42






  • 4




    Follow the following link:. google.co.in/url?sa=t&source=web&rct=j&url=http://…
    – RABI KUMAR CHAKRABORTY
    Nov 28 '18 at 5:13






  • 5




    According to this MO post, the smallest positive solution is $$smallbegin{align} a &= 4373612677928697257861252602371390152816537558161613618621437993378423467772036;\ b &= 36875131794129999827197811565225474825492979968971970996283137471637224634055579;\ c &= 154476802108746166441951315019919837485664325669565431700026634898253202035277999; end{align}$$ This is definitely not a algebra-precalculus/contest problem.
    – achille hui
    Nov 28 '18 at 9:56










  • Oh lol, so I've been bamboozled. Thanks for the answers though, it's interesting reading.
    – Mat Stornel
    Nov 28 '18 at 15:03








5




5




What are trying to minimize? Is it $a + b + c$?
– Alex Vong
Nov 28 '18 at 4:42




What are trying to minimize? Is it $a + b + c$?
– Alex Vong
Nov 28 '18 at 4:42




4




4




Follow the following link:. google.co.in/url?sa=t&source=web&rct=j&url=http://…
– RABI KUMAR CHAKRABORTY
Nov 28 '18 at 5:13




Follow the following link:. google.co.in/url?sa=t&source=web&rct=j&url=http://…
– RABI KUMAR CHAKRABORTY
Nov 28 '18 at 5:13




5




5




According to this MO post, the smallest positive solution is $$smallbegin{align} a &= 4373612677928697257861252602371390152816537558161613618621437993378423467772036;\ b &= 36875131794129999827197811565225474825492979968971970996283137471637224634055579;\ c &= 154476802108746166441951315019919837485664325669565431700026634898253202035277999; end{align}$$ This is definitely not a algebra-precalculus/contest problem.
– achille hui
Nov 28 '18 at 9:56




According to this MO post, the smallest positive solution is $$smallbegin{align} a &= 4373612677928697257861252602371390152816537558161613618621437993378423467772036;\ b &= 36875131794129999827197811565225474825492979968971970996283137471637224634055579;\ c &= 154476802108746166441951315019919837485664325669565431700026634898253202035277999; end{align}$$ This is definitely not a algebra-precalculus/contest problem.
– achille hui
Nov 28 '18 at 9:56












Oh lol, so I've been bamboozled. Thanks for the answers though, it's interesting reading.
– Mat Stornel
Nov 28 '18 at 15:03




Oh lol, so I've been bamboozled. Thanks for the answers though, it's interesting reading.
– Mat Stornel
Nov 28 '18 at 15:03










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