Question

Inequality with square roots conditions

score 124 · Answer 1 · 2019-09-29 00:11:05

124

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Inequality with square roots conditions

Published on 29 Sep 2019 - 0:11

score 3.2k · Answer 2 · 2026-03-21 23:18:47

3.2k

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Proof of the inequality $\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b} \geq \frac{3}{2}$

Published on 21 Mar 2026 - 23:18

score 470 · Answer 3 · 2026-03-21 20:34:23

470

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Prove $\frac{a^3}{b^2}+\frac{b^3}{c^2}+\frac{c^3}{a^2} \geq \frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a}$

Published on 21 Mar 2026 - 20:34

score 197 · Answer 4 · 2026-03-22 06:21:15

197

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symetric inequality for a rational function of three variables

Published on 22 Mar 2026 - 6:21

score 146 · Answer 5 · 2026-03-19 15:12:45

146

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Nesbitt by Nesbitt

Published on 19 Mar 2026 - 15:12

score 112 · Answer 6 · 2019-10-05 17:35:50

112

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Show that every nonnegative polynomial $P \in \mathbb R [x]$ can be written as a sum of squares of real polynomials

Published on 05 Oct 2019 - 17:35

score 294 · Answer 7 · 2019-10-11 14:58:34

294

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Inequality : $\frac{a}{\exp(a+b)}+\frac{b}{\exp(b+c)}+\frac{c}{\exp(c+a)}\leq \exp\Big(\frac{-2}{3}\Big)$

Published on 11 Oct 2019 - 14:58

score 149 · Answer 8 · 2019-10-20 16:26:34

149

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Prove the given inequality if $a+b+c=1$

Published on 20 Oct 2019 - 16:26

score 75 · Answer 9 · 2019-11-13 10:52:07

75

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Prove that $\frac{a}{b} + \frac{b}{c} + \frac{c}{a}$ $\geq$ $\frac{1}{a} + \frac{1}{b} + \frac{1}{c}$

Published on 13 Nov 2019 - 10:52

score 53 · Answer 10 · 2019-11-26 22:01:27

53

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Minimizing the cyclic sum $\sum_{\text{cyc}} \sqrt{\frac{a}{b+c}}$

Published on 26 Nov 2019 - 22:01

score 175 · Answer 11 · 2019-12-03 21:37:34

175

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$x,y,z>0$, prove:$\frac{x}{y+z+\sqrt[4]\frac{y^4+z^4}{2}}+\frac{y}{z+x+\sqrt[4]\frac{z^4+x^4}{2}}+\frac{z}{x+y+\sqrt[4]\frac{x^4+y^4}{2}}\geq1$

Published on 03 Dec 2019 - 21:37

score 187 · Answer 12 · 2019-12-12 20:29:05

187

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How to prove $\sqrt{(a-1)(b-1)}+\sqrt{(a-1)(c-1)}+\sqrt{(b-1)(c-1)}\geq a+b+c+\sqrt{ab}+\sqrt{ac}+\sqrt{bc}$?

Published on 12 Dec 2019 - 20:29

score 169 · Answer 13 · 2019-12-29 09:14:45

169

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Inequality $\frac{x^3}{x^2+y^2}+\frac{y^3}{y^2+z^2}+\frac{z^3}{z^2+x^2} \geqslant \frac{x+y+z}{2}$

Published on 29 Dec 2019 - 9:14

score 90 · Answer 14 · 2020-01-04 14:04:14

90

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Prove that for all acute triangles $\triangle ABC$, $r_a + r_b + r_c \ge m_a + m_b + m_c$.

Published on 04 Jan 2020 - 14:04

score 225 · Answer 15 · 2020-01-08 08:46:15

225

Views

Help with inequality problem

Published on 08 Jan 2020 - 8:46

List Question

Inequality with square roots conditions

Proof of the inequality $\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b} \geq \frac{3}{2}$

Prove $\frac{a^3}{b^2}+\frac{b^3}{c^2}+\frac{c^3}{a^2} \geq \frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a}$

symetric inequality for a rational function of three variables

Nesbitt by Nesbitt

Show that every nonnegative polynomial $P \in \mathbb R [x]$ can be written as a sum of squares of real polynomials

Inequality : $\frac{a}{\exp(a+b)}+\frac{b}{\exp(b+c)}+\frac{c}{\exp(c+a)}\leq \exp\Big(\frac{-2}{3}\Big)$

Prove the given inequality if $a+b+c=1$

Prove that $\frac{a}{b} + \frac{b}{c} + \frac{c}{a}$ $\geq$ $\frac{1}{a} + \frac{1}{b} + \frac{1}{c}$

Minimizing the cyclic sum $\sum_{\text{cyc}} \sqrt{\frac{a}{b+c}}$

$x,y,z>0$, prove:$\frac{x}{y+z+\sqrt[4]\frac{y^4+z^4}{2}}+\frac{y}{z+x+\sqrt[4]\frac{z^4+x^4}{2}}+\frac{z}{x+y+\sqrt[4]\frac{x^4+y^4}{2}}\geq1$

How to prove $\sqrt{(a-1)(b-1)}+\sqrt{(a-1)(c-1)}+\sqrt{(b-1)(c-1)}\geq a+b+c+\sqrt{ab}+\sqrt{ac}+\sqrt{bc}$?

Inequality $\frac{x^3}{x^2+y^2}+\frac{y^3}{y^2+z^2}+\frac{z^3}{z^2+x^2} \geqslant \frac{x+y+z}{2}$

Prove that for all acute triangles $\triangle ABC$, $r_a + r_b + r_c \ge m_a + m_b + m_c$.

Help with inequality problem

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