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

Published on 02 Mar 2020 - 10:45

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Prove that if $a,b,c > 0$ and $a + b + c = 1$, we have: $\frac{a^2}{a^3 + 5} + \frac{b^2}{b^3 + 5} + \frac{c^2}{c^3 + 5} \leq \frac{1}{4}$

Published on 03 Mar 2020 - 14:46

93

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The AM–GM equality

Published on 05 Mar 2020 - 13:23

51

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Exponential equals rational fraction $2^{-3x^3+5x^2-x}=\frac{x^2+1}{x}$

Published on 07 Mar 2020 - 20:10

130

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$\log_{yz} \left(\frac{x^2+4}{4\sqrt{yz}}\right)+\log_{zx}\left(\frac{y^2+4}{4\sqrt{zx}}\right)+\log_{xy}\left(\frac{z^2+4}{4\sqrt{xy}}\right)=0$

Published on 07 Mar 2020 - 21:23

111

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How should I solve these inequalities?

Published on 09 Mar 2020 - 4:56

53

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Inequality Confusion, please guide me.

Published on 09 Mar 2020 - 18:21

258

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The minimum value of $ x_{1}+\frac{x_{2}^{2}}{2}+\frac{x_{3}^{3}}{3}+\ldots+\frac{x_{n}^{n}}{n}$ if $n$ is a positive integer

Published on 10 Mar 2020 - 6:47

121

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Prove that $a^b\cdot b^c \cdot c^a \leq 1$

Published on 12 Mar 2020 - 9:28

128

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Interpreting an olympiad inequality as a convex function

Published on 16 Mar 2020 - 13:32

64

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How Can I Solve This Inequality Using Environmental Inequality?

Published on 16 Mar 2020 - 16:39

61

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Proving the inequality using am gm theorem

Published on 17 Mar 2020 - 4:21

56

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Prove the following inequality using am gm inequality

Published on 25 Mar 2026 - 12:38

170

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Prove that $\frac1{a(1+b)}+\frac1{b(1+c)}+\frac1{c(1+a)}\ge\frac3{1+abc}$

Published on 21 Mar 2020 - 7:08

125

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If $abcd=1$ prove that $\frac{1+ab}{1+a}+\frac{1+bc}{1+b}+\frac{1+cd}{1+c}+\frac{1+ad}{1+d} \ge 4$

Published on 22 Mar 2020 - 6:53

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Bounding roots of a parabola

Prove that if $a,b,c > 0$ and $a + b + c = 1$, we have: $\frac{a^2}{a^3 + 5} + \frac{b^2}{b^3 + 5} + \frac{c^2}{c^3 + 5} \leq \frac{1}{4}$

The AM–GM equality

Exponential equals rational fraction $2^{-3x^3+5x^2-x}=\frac{x^2+1}{x}$

$\log_{yz} \left(\frac{x^2+4}{4\sqrt{yz}}\right)+\log_{zx}\left(\frac{y^2+4}{4\sqrt{zx}}\right)+\log_{xy}\left(\frac{z^2+4}{4\sqrt{xy}}\right)=0$

How should I solve these inequalities?

Inequality Confusion, please guide me.

The minimum value of $ x_{1}+\frac{x_{2}^{2}}{2}+\frac{x_{3}^{3}}{3}+\ldots+\frac{x_{n}^{n}}{n}$ if $n$ is a positive integer

Prove that $a^b\cdot b^c \cdot c^a \leq 1$

Interpreting an olympiad inequality as a convex function

How Can I Solve This Inequality Using Environmental Inequality?

Proving the inequality using am gm theorem

Prove the following inequality using am gm inequality

Prove that $\frac1{a(1+b)}+\frac1{b(1+c)}+\frac1{c(1+a)}\ge\frac3{1+abc}$

If $abcd=1$ prove that $\frac{1+ab}{1+a}+\frac{1+bc}{1+b}+\frac{1+cd}{1+c}+\frac{1+ad}{1+d} \ge 4$

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