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.
algebra-precalculus contest-math algebraic-number-theory
asked Nov 28 '18 at 4:37
Mat Stornel
111
add a comment |
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.
algebra-precalculus contest-math algebraic-number-theory
asked Nov 28 '18 at 4:37
Mat Stornel
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
add a comment |
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.
algebra-precalculus contest-math algebraic-number-theory
asked Nov 28 '18 at 4:37
Mat Stornel
111
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
algebra-precalculus contest-math algebraic-number-theory
asked Nov 28 '18 at 4:37
Mat Stornel
111
asked Nov 28 '18 at 4:37
Mat Stornel
111
asked Nov 28 '18 at 4:37
Mat Stornel
111
asked Nov 28 '18 at 4:37
Mat Stornel
111
asked Nov 28 '18 at 4:37
Mat 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
add a comment |
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
add a comment |
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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