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

Published on 01 Mar 2017 - 16:15

270

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For $a,b,c$. Prove that $\frac{a^2}{a+\sqrt[3]{bc}}+\frac{b^2}{b+\sqrt[3]{ca}}+\frac{c^2}{c+\sqrt[3]{ab}}\ge\frac{3}{2}$

Published on 08 Mar 2017 - 4:13

166

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If $x,y>0$ and $x^2+y^3\ge x^3+y^4$, prove that $x^3+y^3 \le 2$.

Published on 09 Mar 2017 - 7:08

48

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About an inequality

Published on 10 Mar 2017 - 17:28

114

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Help understanding AM-GM use.

Published on 10 Mar 2017 - 23:20

151

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A nice use of $AM GM HM$ inequality

Published on 11 Mar 2017 - 7:31

1.2k

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The geometric mean and the arithmetic mean of two positive numbers

Published on 12 Mar 2017 - 15:30

672

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Find the maximum of the value $F=x_{1}x_{2}x_{3}+x_{2}x_{3}x_{4}+\cdots+x_{n-2}x_{n-1}x_{n}+x_{n-1}x_{n}x_{1}$

Published on 16 Mar 2017 - 5:24

738

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How do I find the maximum value of $x^{\ln y}$?

Published on 18 Mar 2017 - 8:17

1.1k

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To find the greatest value of a product whose sum is constant

Published on 18 Mar 2017 - 14:30

124

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Determine the minimum value of the expression, for $a,b$ , $c$ $\in\ \textbf{R}^+$

Published on 19 Mar 2017 - 13:10

1.5k

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If $x^2 + y^2 + z^2 + 2xyz = 1$ then $x+ y+ z \leq \frac{3}{2}?$

Published on 19 Mar 2017 - 14:08

474

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AM-GM giving wrong result on applying to trigonometric functions

Published on 22 Mar 2017 - 5:35

419

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Prove this Generalizing AM-GM inequality

Published on 23 Mar 2017 - 12:56

148

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Let $a,b,c$ be positive numbers. Prove that $a^2b+b^2c+c^2a\leq a^3+b^3+c^3$

Published on 25 Mar 2026 - 17:19

List Question

Inequalities help: $(a^3+b^3)^2\leq (a^2+b^2)(a^4+b^4)$

For $a,b,c$. Prove that $\frac{a^2}{a+\sqrt[3]{bc}}+\frac{b^2}{b+\sqrt[3]{ca}}+\frac{c^2}{c+\sqrt[3]{ab}}\ge\frac{3}{2}$

If $x,y>0$ and $x^2+y^3\ge x^3+y^4$, prove that $x^3+y^3 \le 2$.

About an inequality

Help understanding AM-GM use.

A nice use of $AM GM HM$ inequality

The geometric mean and the arithmetic mean of two positive numbers

Find the maximum of the value $F=x_{1}x_{2}x_{3}+x_{2}x_{3}x_{4}+\cdots+x_{n-2}x_{n-1}x_{n}+x_{n-1}x_{n}x_{1}$

How do I find the maximum value of $x^{\ln y}$?

To find the greatest value of a product whose sum is constant

Determine the minimum value of the expression, for $a,b$ , $c$ $\in\ \textbf{R}^+$

If $x^2 + y^2 + z^2 + 2xyz = 1$ then $x+ y+ z \leq \frac{3}{2}?$

AM-GM giving wrong result on applying to trigonometric functions

Prove this Generalizing AM-GM inequality

Let $a,b,c$ be positive numbers. Prove that $a^2b+b^2c+c^2a\leq a^3+b^3+c^3$

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