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

Published on 25 Mar 2026 - 14:33

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Prove inequality by inequality of means

Published on 25 Mar 2026 - 12:53

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

166

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Maximum value of $\frac{x}{y+1}+\frac{y}{x+1}$ while $0\leq x,y \leq 1$

Published on 14 Dec 2019 - 12:27

73

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Inequality $\sum_{cyc}a^3\frac{(16a^2-10ab+12b^2)}{(13a^2+5b^2)^2}\geq \frac{a+b+c}{18}$

Published on 18 Dec 2019 - 10:05

112

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Proving inequality $(a^2 + b^2)^3 \ge 32(a^3 + b^3)(ab - a - b)$

Published on 27 Mar 2026 - 2:37

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Proving $\frac{a}{a^2+2b^2}+\frac{b}{b^2+2c^2}+\frac{c}{c^2+2a^2}\geq 1$ when $a^2+b^2+c^2=a^3+b^3+c^3$

Published on 18 Dec 2019 - 18:25

230

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How to prove $\frac{a}{7a+b}+\frac{b}{7b+c}+\frac{c}{7c+a}\le\frac38$

Published on 20 Dec 2019 - 22:37

32

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How to estimate upper bound of $|\frac{3h^2k}{6(h^2+k^2)^{3/2}}|$ to $\frac{3}{6}?$

Published on 29 Dec 2019 - 12:03

197

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Is there an accepted strategy when tackling proofs involving inequalities?

Published on 03 Jan 2020 - 2:17

190

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How is AM-GM supposed to be used to prove an inequality

Published on 04 Jan 2020 - 23:24

43

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An algebraic inequality for $\delta,q\in(0,1)$

Published on 06 Jan 2020 - 15:16

170

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Can every inequality be proved using the AM-GM inequality?

Published on 06 Jan 2020 - 22:58

69

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For real numbers $x>0, y>0, z>0$ and $x y z=1 .$ prove that $ x^{6}+y^{6}+z^{6} \geq x^{5}+y^{5}+z^{5} $

Published on 25 Mar 2026 - 9:43

94

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Proving an inequality using cases and the AM-GM inequality

Published on 08 Jan 2020 - 0:28

List Question

Inequality Proof $(x^2+1)(y^2+1)(z^2+1)\leq...$

Prove inequality by inequality of means

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

Maximum value of $\frac{x}{y+1}+\frac{y}{x+1}$ while $0\leq x,y \leq 1$

Inequality $\sum_{cyc}a^3\frac{(16a^2-10ab+12b^2)}{(13a^2+5b^2)^2}\geq \frac{a+b+c}{18}$

Proving inequality $(a^2 + b^2)^3 \ge 32(a^3 + b^3)(ab - a - b)$

Proving $\frac{a}{a^2+2b^2}+\frac{b}{b^2+2c^2}+\frac{c}{c^2+2a^2}\geq 1$ when $a^2+b^2+c^2=a^3+b^3+c^3$

How to prove $\frac{a}{7a+b}+\frac{b}{7b+c}+\frac{c}{7c+a}\le\frac38$

How to estimate upper bound of $|\frac{3h^2k}{6(h^2+k^2)^{3/2}}|$ to $\frac{3}{6}?$

Is there an accepted strategy when tackling proofs involving inequalities?

How is AM-GM supposed to be used to prove an inequality

An algebraic inequality for $\delta,q\in(0,1)$

Can every inequality be proved using the AM-GM inequality?

For real numbers $x>0, y>0, z>0$ and $x y z=1 .$ prove that $ x^{6}+y^{6}+z^{6} \geq x^{5}+y^{5}+z^{5} $

Proving an inequality using cases and the AM-GM inequality

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