Question

Prove a geometric inequality, if 3 numbers are satisfying the condition

score 100 · Answer 1 · 2026-03-26 14:43:03

100

Views

Prove a geometric inequality, if 3 numbers are satisfying the condition

Published on 26 Mar 2026 - 14:43

score 73 · Answer 2 · 2026-03-25 15:46:16

73

Views

Simple symmetric inequality involving four variables

Published on 25 Mar 2026 - 15:46

score 79 · Answer 3 · 2016-08-30 12:36:52

79

Views

show that $\frac{c^2}{a}+\frac{a^2}{c}+16\sqrt{ac}\ge 9(a+c)$

Published on 30 Aug 2016 - 12:36

score 275 · Answer 4 · 2026-03-25 15:44:11

275

Views

Prove the inequality $\left(\frac1a+\frac1b+\frac1c\right)\left(\frac1{1+a}+\frac1{1+b}+\frac1{1+c}\right)\ge\frac9{1+abc}$

Published on 25 Mar 2026 - 15:44

score 418 · Answer 5 · 2026-03-25 23:39:30

418

Views

Prove that $(1+a_1) \cdot (1+a_2) \cdot \dots \cdot (1+a_n) \geq 2^n$

Published on 25 Mar 2026 - 23:39

score 180 · Answer 6 · 2026-03-26 01:17:56

180

Views

Proof of this simple inequality: $\frac{a}{b} + \frac{b}{c} + \frac{c}{d} + \frac{d}{a} \geq 4$

Published on 26 Mar 2026 - 1:17

score 111 · Answer 7 · 2016-09-11 01:00:24

111

Views

inequality for positive number $a+b+c=3$

Published on 11 Sep 2016 - 1:00

score 617 · Answer 8 · 2016-09-11 08:56:47

617

Views

Proof of quadratic inequality using AM-GM

Published on 11 Sep 2016 - 8:56

score 100 · Answer 9 · 2016-09-19 17:53:27

100

Views

Largest k for $\displaystyle (a+b+c)^5 \ge\frac{k}{\sqrt{5}}(ab+bc+ca)(a-b)(b-c)(c-a)$

Published on 19 Sep 2016 - 17:53

score 116 · Answer 10 · 2026-03-28 08:27:59

116

Views

Generalizing proof of AM-GM inequality?

Published on 28 Mar 2026 - 8:27

score 82 · Answer 11 · 2016-09-28 21:58:36

82

Views

If $a,b,c>0$ and $a^3+b^3=c^3$ then prove that $a^2+b^2-c^2>6(c-a)(c-b)$.

Published on 28 Sep 2016 - 21:58

score 89 · Answer 12 · 2016-10-02 04:55:46

89

Views

If $a+b=1$ where $a,b\in\Bbb R^+$ then prove that $a^ab^b+b^aa^b\le1$

Published on 02 Oct 2016 - 4:55

score 92 · Answer 13 · 2016-10-02 11:49:36

92

Views

Prove that $\frac{\sqrt{\prod_{i=1}^n}x_i}{n-1} \geq 1998$

Published on 02 Oct 2016 - 11:49

score 296 · Answer 14 · 2016-10-05 15:44:07

296

Views

If $a$, $b$ and $c$ are three positive real numbers, prove that $\frac{a^2+1}{b+c}+\frac{b^2+1}{c+a}+\frac{c^2+1}{a+b} ≥ 3$

Published on 05 Oct 2016 - 15:44

score 478 · Answer 15 · 2016-10-08 01:51:18

478

Views

Prove that $ab+bc+cd \le \frac{1}{4} $ if $a+b+c+d =1$

Published on 08 Oct 2016 - 1:51

List Question

Prove a geometric inequality, if 3 numbers are satisfying the condition

Simple symmetric inequality involving four variables

show that $\frac{c^2}{a}+\frac{a^2}{c}+16\sqrt{ac}\ge 9(a+c)$

Prove the inequality $\left(\frac1a+\frac1b+\frac1c\right)\left(\frac1{1+a}+\frac1{1+b}+\frac1{1+c}\right)\ge\frac9{1+abc}$

Prove that $(1+a_1) \cdot (1+a_2) \cdot \dots \cdot (1+a_n) \geq 2^n$

Proof of this simple inequality: $\frac{a}{b} + \frac{b}{c} + \frac{c}{d} + \frac{d}{a} \geq 4$

inequality for positive number $a+b+c=3$

Proof of quadratic inequality using AM-GM

Largest k for $\displaystyle (a+b+c)^5 \ge\frac{k}{\sqrt{5}}(ab+bc+ca)(a-b)(b-c)(c-a)$

Generalizing proof of AM-GM inequality?

If $a,b,c>0$ and $a^3+b^3=c^3$ then prove that $a^2+b^2-c^2>6(c-a)(c-b)$.

If $a+b=1$ where $a,b\in\Bbb R^+$ then prove that $a^ab^b+b^aa^b\le1$

Prove that $\frac{\sqrt{\prod_{i=1}^n}x_i}{n-1} \geq 1998$

If $a$, $b$ and $c$ are three positive real numbers, prove that $\frac{a^2+1}{b+c}+\frac{b^2+1}{c+a}+\frac{c^2+1}{a+b} ≥ 3$

Prove that $ab+bc+cd \le \frac{1}{4} $ if $a+b+c+d =1$

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