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Martin Sleziak
Martin Sleziak
6:03 AM
 
 
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Martin Sleziak
Martin Sleziak
5:38 PM
new-tag The tag sos is list among new tags after a question was undeleted.
-3
Q: Triangle inequality $\frac{ab}{a^{2}+ b^{2}}+ \frac{bc}{b^{2}+ c^{2}}+ \frac{ca}{c^{2}+ a^{2}}\geq \frac{1}{2}+ \frac{2r}{R}$

Gang_JiHaSuppose that $a, b, c$ be the lengths of 3 sides of a triangle. Prove that $$\frac{ab}{a^{2}+ b^{2}}+ \frac{bc}{b^{2}+ c^{2}}+ \frac{ca}{c^{2}+ a^{2}}\geq \frac{1}{2}+ \frac{2r}{R}$$ It' s so amazing, I tried to use Euler and Gerretsen' s inequality. It' s difficult to me. Help me!

geometry inequality fractions geometric-inequalities sos
As far as I can tell, this tag was created and removed before: chat.stackexchange.com/search?room=3740&q=sos chat.stackexchange.com/…
Posts where the tag sos was added/removed (including the editors): data.stackexchange.com/math/query/1105163/… data.stackexchange.com/math/query/1038474/…
 
Martin Sleziak
Martin Sleziak
6:12 PM
-3
Q: Triangle inequality $\frac{ab}{a^{2}+ b^{2}}+ \frac{bc}{b^{2}+ c^{2}}+ \frac{ca}{c^{2}+ a^{2}}\geq \frac{1}{2}+ \frac{2r}{R}$

Gang_JiHaSuppose that $a, b, c$ be the lengths of 3 sides of a triangle. Prove that $$\frac{ab}{a^{2}+ b^{2}}+ \frac{bc}{b^{2}+ c^{2}}+ \frac{ca}{c^{2}+ a^{2}}\geq \frac{1}{2}+ \frac{2r}{R}$$ It' s so amazing, I tried to use Euler and Gerretsen' s inequality. It' s difficult to me. Help me!

geometry inequality fractions geometric-inequalities sum-of-squares-method
 

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