Question

Inequality with square roots conditions

score 126 · Answer 1 · 2026-04-01 13:00:36

126

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Inequality with square roots conditions

Published on 01 Apr 2026 - 13:00

score 3.2k · Answer 2 · 2026-03-25 11:04:55

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 25 Mar 2026 - 11:04

score 471 · Answer 3 · 2026-03-25 11:04:55

471

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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 25 Mar 2026 - 11:04

score 198 · Answer 4 · 2026-03-25 11:01:25

198

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symetric inequality for a rational function of three variables

Published on 25 Mar 2026 - 11:01

score 162 · Answer 5 · 2026-04-26 09:55:47

162

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Nesbitt by Nesbitt

Published on 26 Apr 2026 - 9:55

score 113 · Answer 6 · 2026-04-23 22:21:12

113

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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 23 Apr 2026 - 22:21

score 295 · Answer 7 · 2026-04-06 08:07:00

295

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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 06 Apr 2026 - 8:07

score 151 · Answer 8 · 2026-04-17 09:28:47

151

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

Published on 17 Apr 2026 - 9:28

score 76 · Answer 9 · 2026-03-25 11:04:31

76

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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 25 Mar 2026 - 11:04

score 54 · Answer 10 · 2026-03-25 11:01:47

54

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

Published on 25 Mar 2026 - 11:01

score 176 · Answer 11 · 2026-03-25 11:04:50

176

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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 25 Mar 2026 - 11:04

score 188 · Answer 12 · 2026-03-25 11:04:54

188

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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 25 Mar 2026 - 11:04

score 170 · Answer 13 · 2026-05-01 19:04:14

170

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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 01 May 2026 - 19:04

score 91 · Answer 14 · 2026-03-25 11:06:31

91

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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 25 Mar 2026 - 11:06

score 228 · Answer 15 · 2026-05-10 15:58:44

228

Views

Help with inequality problem

Published on 10 May 2026 - 15:58

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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