Question

If $a, b, c\in\mathbb R^+,$ then prove that: $\sum_{cyc} \frac1{c-b}\left(\frac1{\sqrt{a+2b}}-\frac1{\sqrt{a+2c}}\right)\ge\frac3{\sqrt{(a+b+c)^3}}.$

score 68 · Answer 1 · 2026-03-25 23:42:24

68

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If $a, b, c\in\mathbb R^+,$ then prove that: $\sum_{cyc} \frac1{c-b}\left(\frac1{\sqrt{a+2b}}-\frac1{\sqrt{a+2c}}\right)\ge\frac3{\sqrt{(a+b+c)^3}}.$

Published on 25 Mar 2026 - 23:42

score 180 · Answer 2 · 2026-03-25 06:06:51

180

Views

If $\frac{1}{1+a}+\frac{1}{1+b}+\frac{1}{1+c}\le 1$, prove that $(1+a^2)(1+b^2)(1+c^2)\ge 125$.

Published on 25 Mar 2026 - 6:06

score 133 · Answer 3 · 2020-07-21 04:24:40

133

Views

Strange Cube Root Offense in an Inequality

Published on 21 Jul 2020 - 4:24

score 117 · Answer 4 · 2026-02-23 04:41:38

117

Views

On Resolving a Fuss on Squares and Fractions over a few Inequalities

Published on 23 Feb 2026 - 4:41

score 104 · Answer 5 · 2020-07-23 05:56:09

104

Views

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score 74 · Answer 6 · 2020-07-26 05:19:48

74

Views

Prove the inequality $u^{\alpha}v^{1-\alpha} \leq \alpha u + (1-\alpha)v $

Published on 26 Jul 2020 - 5:19

score 238 · Answer 7 · 2020-07-26 07:26:09

238

Views

Maximum of $\sum_{cyc}x_1x_2x_3\cdots x_k$ given $x_1+x_2+\ldots+x_n=a$ for non-negative $x_1,\ldots,x_n$ for a positive integer $n$ and $1<k<n$

Published on 26 Jul 2020 - 7:26

score 49 · Answer 8 · 2026-03-25 20:41:08

49

Views

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Published on 25 Mar 2026 - 20:41

score 57 · Answer 9 · 2020-07-26 14:31:27

57

Views

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score 114 · Answer 10 · 2020-07-27 13:02:47

114

Views

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score 80 · Answer 11 · 2020-07-30 09:35:00

80

Views

Finding a Mistake for a Particular Form of Inequality

Published on 30 Jul 2020 - 9:35

score 840 · Answer 12 · 2026-03-25 09:29:57

840

Views

If $a$, $b$, $c$, $d$ are positive reals so $(a+c)(b+d) = 1$, prove the following inequality would be greater than or equal to $\frac {1}{3}$.

Published on 25 Mar 2026 - 9:29

score 3.3k · Answer 13 · 2016-07-07 07:35:28

3.3k

Views

Using AM-GM Inequality (Arithmetic mean- Geometric Mean) Find the minimum value of $2x^2+\frac{1}{x^4}$

Published on 07 Jul 2016 - 7:35

score 225 · Answer 14 · 2016-07-11 16:31:06

225

Views

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Published on 11 Jul 2016 - 16:31

score 240 · Answer 15 · 2016-07-20 20:30:43

240

Views

Upper bound of $x_1x_2x_3+x_2x_3x_4+\dots+x_{n}x_1x_2$

Published on 20 Jul 2016 - 20:30

List Question

If $a, b, c\in\mathbb R^+,$ then prove that: $\sum_{cyc} \frac1{c-b}\left(\frac1{\sqrt{a+2b}}-\frac1{\sqrt{a+2c}}\right)\ge\frac3{\sqrt{(a+b+c)^3}}.$

If $\frac{1}{1+a}+\frac{1}{1+b}+\frac{1}{1+c}\le 1$, prove that $(1+a^2)(1+b^2)(1+c^2)\ge 125$.

Strange Cube Root Offense in an Inequality

On Resolving a Fuss on Squares and Fractions over a few Inequalities

Problem with $A.M.\geq G.M.$ Inequality

Prove the inequality $u^{\alpha}v^{1-\alpha} \leq \alpha u + (1-\alpha)v $

Maximum of $\sum_{cyc}x_1x_2x_3\cdots x_k$ given $x_1+x_2+\ldots+x_n=a$ for non-negative $x_1,\ldots,x_n$ for a positive integer $n$ and $1<k<n$

Obliterating Squares and Roots

Asymmetric, Unusually Restricted Inequality

Hint to an Inequality

Finding a Mistake for a Particular Form of Inequality

If $a$, $b$, $c$, $d$ are positive reals so $(a+c)(b+d) = 1$, prove the following inequality would be greater than or equal to $\frac {1}{3}$.

Using AM-GM Inequality (Arithmetic mean- Geometric Mean) Find the minimum value of $2x^2+\frac{1}{x^4}$

Prove an inequality by Second partial derivative test?

Upper bound of $x_1x_2x_3+x_2x_3x_4+\dots+x_{n}x_1x_2$

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