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

Published on 27 Feb 2013 - 8:08

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Prove the A-G-M Inequality using Lagrange multipliers.

Published on 13 Mar 2013 - 4:58

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Prove $\sqrt{a} + \sqrt{b} + \sqrt{c} \ge ab + bc + ca$

Published on 25 Mar 2026 - 15:40

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Prove $\sqrt{3a + b^3} + \sqrt{3b + c^3} + \sqrt{3c + a^3} \ge 6$

Published on 20 Mar 2013 - 23:21

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A more elementary proof that if $x_i>0$ for $1\leq i\leq n$, and $\sum x_i=1$, then $(x_1+\frac{1}{x_1})\cdots(x_n+\frac{1}{x_n})\geq(n+\frac1n)^n$

Published on 25 Mar 2026 - 15:44

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Inequality with a High Degree Constraint

Published on 25 Mar 2026 - 15:39

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If $a^2 + b^2 + c^2 = 1$, what is the the minimum value of $\frac {ab}{c} + \frac {bc}{a} + \frac {ca}{b}$?

Published on 25 Mar 2026 - 21:54

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Why does AM>GM when applied on functions gives the absolute minima.

Published on 05 Aug 2020 - 3:59

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Maximum Value of Product of powers of Positive Numbers

Published on 28 Mar 2026 - 18:17

69

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If $xyz=32$, find the minimal value of

Published on 06 Aug 2020 - 14:46

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Spivak AMGM exercise

Published on 06 Aug 2020 - 19:15

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$ax^2 -bx +c =0$ where $a,b,c$ are natural nos. and it has roots lying in the interval $(1,2)$...

Published on 08 Aug 2020 - 14:41

138

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find maximum value of $\frac x{(x^2+1)^{\frac32}}$ with AM-GM inequality

Published on 10 Aug 2020 - 10:51

142

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Verifying a proof that $\frac{x^2}{y^3}+\frac{y^2}{z^3}+\frac{z^2}{x^3}≥x^2+y^2+z^2$ when $xyz=1$ and x,y,z are positive real number

Published on 11 Aug 2020 - 12:30

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Let $x, y, z$ be positive distinct integers. Prove that $(x+y+z)(xy+yz+zx-2)\ge9xyz$

Published on 11 Aug 2020 - 15:53

List Question

Simple AM-GM inequality

Prove the A-G-M Inequality using Lagrange multipliers.

Prove $\sqrt{a} + \sqrt{b} + \sqrt{c} \ge ab + bc + ca$

Prove $\sqrt{3a + b^3} + \sqrt{3b + c^3} + \sqrt{3c + a^3} \ge 6$

A more elementary proof that if $x_i>0$ for $1\leq i\leq n$, and $\sum x_i=1$, then $(x_1+\frac{1}{x_1})\cdots(x_n+\frac{1}{x_n})\geq(n+\frac1n)^n$

Inequality with a High Degree Constraint

If $a^2 + b^2 + c^2 = 1$, what is the the minimum value of $\frac {ab}{c} + \frac {bc}{a} + \frac {ca}{b}$?

Why does AM>GM when applied on functions gives the absolute minima.

Maximum Value of Product of powers of Positive Numbers

If $xyz=32$, find the minimal value of

Spivak AMGM exercise

$ax^2 -bx +c =0$ where $a,b,c$ are natural nos. and it has roots lying in the interval $(1,2)$...

find maximum value of $\frac x{(x^2+1)^{\frac32}}$ with AM-GM inequality

Verifying a proof that $\frac{x^2}{y^3}+\frac{y^2}{z^3}+\frac{z^2}{x^3}≥x^2+y^2+z^2$ when $xyz=1$ and x,y,z are positive real number

Let $x, y, z$ be positive distinct integers. Prove that $(x+y+z)(xy+yz+zx-2)\ge9xyz$

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