List questions from a-m-g-m-inequality

194

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Prove that $\frac{bc}{a^2+bc}+\frac{ca}{b^2+ca}+\frac{ab}{c^2+ab}\le{\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b}}$

Published on 08 Jan 2016 - 11:13

81

Views

Find the minimum of $\sum\limits_{cyc} {\sqrt{\frac a{2(b+c)}}}$ with $a,b,c \gt 0$

Published on 21 Mar 2026 - 21:53

202

Views

Prove that $\left | \frac{a-b}{a+b}+\frac{b-c}{b+c}+\frac{c-a}{c+a} \right | < \frac{1}{8}.$

Published on 21 Jan 2016 - 15:52

355

Views

How to prove $\sqrt{\frac{bc}{a+bc}}+\sqrt{\frac{ca}{b+ca}}+\sqrt{\frac{ab}{c+ab}}\geq 1$

Published on 30 Jan 2016 - 9:51

104

Views

Prove the inequality $\frac{a^2+b^2}{c^2+a+b}+\frac{b^2+c^2}{a^2+b+c}+\frac{c^2+a^2}{b^2+c+a} \ge 2$

Published on 21 Feb 2016 - 8:51

220

Views

Inequalities - AM-GM

Published on 29 Mar 2026 - 10:07

137

Views

Find a maximum of: $x^{2016} \cdot y+y^{2016} \cdot z+z^{2016} \cdot x $

Published on 09 Mar 2026 - 19:23

1.3k

Views

How to show AM-GM inequality using rearrangement inequality?

Published on 20 Apr 2016 - 12:57

320

Views

Prove this inequality: $\frac{b+c}{\sqrt{a}}+\frac{c+a}{\sqrt{b}}+\frac{a+b}{\sqrt{c}}\geq \sqrt{a}+\sqrt{b}+\sqrt{c}+3$

Published on 21 Apr 2016 - 3:10

118

Views

How do I show that $\frac {\cos^2 A}{\cos^2 B} + \frac {\cos^2 B}{\cos^2 C} + \frac {\cos^2 C}{\cos^2 A} \ge 4(\cos^2 A + \cos^2 B + \cos^2 C)$?

Published on 24 Apr 2016 - 15:01

121

Views

Find the minimum $k$

Published on 29 Mar 2026 - 19:44

253

Views

Geometric inequality involving sides of the triangle

Published on 27 Mar 2026 - 6:56

294

Views

Application of A.M. -G.M. inequality

Published on 29 Mar 2026 - 11:44

64

Views

Algebraic Inequality

Published on 29 Mar 2026 - 20:56

111

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Inequality about sums and products

Published on 02 May 2016 - 19:34

List Question

Prove that $\frac{bc}{a^2+bc}+\frac{ca}{b^2+ca}+\frac{ab}{c^2+ab}\le{\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b}}$

Find the minimum of $\sum\limits_{cyc} {\sqrt{\frac a{2(b+c)}}}$ with $a,b,c \gt 0$

Prove that $\left | \frac{a-b}{a+b}+\frac{b-c}{b+c}+\frac{c-a}{c+a} \right | < \frac{1}{8}.$

How to prove $\sqrt{\frac{bc}{a+bc}}+\sqrt{\frac{ca}{b+ca}}+\sqrt{\frac{ab}{c+ab}}\geq 1$

Prove the inequality $\frac{a^2+b^2}{c^2+a+b}+\frac{b^2+c^2}{a^2+b+c}+\frac{c^2+a^2}{b^2+c+a} \ge 2$

Inequalities - AM-GM

Find a maximum of: $x^{2016} \cdot y+y^{2016} \cdot z+z^{2016} \cdot x $

How to show AM-GM inequality using rearrangement inequality?

Prove this inequality: $\frac{b+c}{\sqrt{a}}+\frac{c+a}{\sqrt{b}}+\frac{a+b}{\sqrt{c}}\geq \sqrt{a}+\sqrt{b}+\sqrt{c}+3$

How do I show that $\frac {\cos^2 A}{\cos^2 B} + \frac {\cos^2 B}{\cos^2 C} + \frac {\cos^2 C}{\cos^2 A} \ge 4(\cos^2 A + \cos^2 B + \cos^2 C)$?

Find the minimum $k$

Geometric inequality involving sides of the triangle

Application of A.M. -G.M. inequality

Algebraic Inequality

Inequality about sums and products

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