Question

Is this alternative proof of the inequality $\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\geq\frac{3}{2}$ correct?

score 160 · Answer 1 · 2026-03-24 05:06:27

160

Views

Is this alternative proof of the inequality $\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\geq\frac{3}{2}$ correct?

Published on 24 Mar 2026 - 5:06

score 159 · Answer 2 · 2026-03-23 18:31:19

159

Views

SOS proof for $\sum_{cyc}\frac{a^3}{bc}\ge a+b+c$

Published on 23 Mar 2026 - 18:31

score 147 · Answer 3 · 2026-03-25 17:42:01

147

Views

Proving $4\Big(\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2} \Big)+\frac{81}{(a+b+c)^2}\geqslant{\frac {7(a+b+c)}{abc}}$

Published on 25 Mar 2026 - 17:42

score 186 · Answer 4 · 2026-02-23 08:07:07

186

Views

Proving $\frac{a}{b^3}+\frac{b}{c^3}+\frac{c}{a^3}\geqslant \frac{a+b}{b^3+c^3}+\frac{b+c}{c^3+a^3}+\frac{c+a}{a^3+b^3}$

Published on 23 Feb 2026 - 8:07

score 77 · Answer 5 · 2026-03-24 02:46:33

77

Views

Proving $2\left(b^2+c^2\right)-a^2\leqslant 12$ with some condition.

Published on 24 Mar 2026 - 2:46

score 175 · Answer 6 · 2026-03-26 16:10:13

175

Views

Prove $\sum ab \sum \frac{1}{(a+b)^2} \geqslant \frac{9}{4}+\frac{kabc\sum (a^2-bc)}{(a+b+c)^3(ab+bc+ca)}$ for the best k.

Published on 26 Mar 2026 - 16:10

score 205 · Answer 7 · 2026-03-23 16:20:40

205

Views

prove $a^3+b^3+c^3+3abc\ge \sum_{cyc}ab(a+b)$

Published on 23 Mar 2026 - 16:20

score 156 · Answer 8 · 2026-03-26 16:07:02

156

Views

Proving $(a+b+c) \Big(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\Big) \leqslant 25$

Published on 26 Mar 2026 - 16:07

score 96 · Answer 9 · 2026-03-25 06:34:58

96

Views

Proving $\sum \frac{a+b}{c} \geq 2.\sqrt{(a+b+c)(\frac{a}{bc} +\frac{b}{ca}+ \frac{c}{ab})}$

Published on 25 Mar 2026 - 6:34

score 110 · Answer 10 · 2026-03-24 08:47:43

110

Views

Proving $\frac{{a}^3+{b}^3+ac(a-c)+bc(b-c)-5abc}{{(a+b+c)}^3} \geqslant -\frac{1}{5}$

Published on 24 Mar 2026 - 8:47

score 360 · Answer 11 · 2026-03-24 15:57:37

360

Views

Proving Markov–Lukacs theorem from SOS programming

Published on 24 Mar 2026 - 15:57

score 139 · Answer 12 · 2026-03-23 18:34:44

139

Views

To Prove $\frac{1}{b}+\frac{1}{c}+\frac{1}{a} > \sqrt{a}+\sqrt{b}+\sqrt{c}$

Published on 23 Mar 2026 - 18:34

score 70 · Answer 13 · 2026-03-23 21:43:08

70

Views

question from Euclid 2011 about proving that $\frac{(a^3+b^3)c}{a^2+b^2}+\frac{(b^3+c^3)a}{b^2+c^2}+\frac{(c^3+a^3)}{c^2+a^2}\ge 1$

Published on 23 Mar 2026 - 21:43

score 105 · Answer 14 · 2026-03-23 16:28:24

105

Views

Symmetric inequality over 3 variables with restriction $a+b+c=1$

Published on 23 Mar 2026 - 16:28

score 153 · Answer 15 · 2026-03-26 11:54:42

153

Views

$\frac{a^3}{b+c}+\frac{b^3}{a+c}+\frac{c^3}{a+b}\geq \frac{3}{2}$ for $a,b,c\in\mathbb{R}^+$ with $abc=1$

Published on 26 Mar 2026 - 11:54

List Question

Is this alternative proof of the inequality $\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\geq\frac{3}{2}$ correct?

SOS proof for $\sum_{cyc}\frac{a^3}{bc}\ge a+b+c$

Proving $4\Big(\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2} \Big)+\frac{81}{(a+b+c)^2}\geqslant{\frac {7(a+b+c)}{abc}}$

Proving $\frac{a}{b^3}+\frac{b}{c^3}+\frac{c}{a^3}\geqslant \frac{a+b}{b^3+c^3}+\frac{b+c}{c^3+a^3}+\frac{c+a}{a^3+b^3}$

Proving $2\left(b^2+c^2\right)-a^2\leqslant 12$ with some condition.

Prove $\sum ab \sum \frac{1}{(a+b)^2} \geqslant \frac{9}{4}+\frac{kabc\sum (a^2-bc)}{(a+b+c)^3(ab+bc+ca)}$ for the best k.

prove $a^3+b^3+c^3+3abc\ge \sum_{cyc}ab(a+b)$

Proving $(a+b+c) \Big(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\Big) \leqslant 25$

Proving $\sum \frac{a+b}{c} \geq 2.\sqrt{(a+b+c)(\frac{a}{bc} +\frac{b}{ca}+ \frac{c}{ab})}$

Proving $\frac{{a}^3+{b}^3+ac(a-c)+bc(b-c)-5abc}{{(a+b+c)}^3} \geqslant -\frac{1}{5}$

Proving Markov–Lukacs theorem from SOS programming

To Prove $\frac{1}{b}+\frac{1}{c}+\frac{1}{a} > \sqrt{a}+\sqrt{b}+\sqrt{c}$

question from Euclid 2011 about proving that $\frac{(a^3+b^3)c}{a^2+b^2}+\frac{(b^3+c^3)a}{b^2+c^2}+\frac{(c^3+a^3)}{c^2+a^2}\ge 1$

Symmetric inequality over 3 variables with restriction $a+b+c=1$

$\frac{a^3}{b+c}+\frac{b^3}{a+c}+\frac{c^3}{a+b}\geq \frac{3}{2}$ for $a,b,c\in\mathbb{R}^+$ with $abc=1$

Trending Questions

Popular # Hahtags

Popular Questions