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

Published on 25 Mar 2026 - 15:47

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values of $a$ in inequality

Published on 04 Feb 2017 - 7:02

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Finding maxima and minima of $f(x,y)= x^4 + y^4 - 2x^2 - 2y^2 + 4xy$

Published on 05 Feb 2017 - 16:09

278

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Proving the inequality $(a^2-ab+b^2)(c^2-ac+a^2)(b^2-bc+c^2) \le 12$.

Published on 28 Mar 2026 - 21:06

148

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Lower bound for $\frac{(x+y+z)^3}{xy+yz+zx}$

Published on 07 Feb 2017 - 4:15

82

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Which is the correct way to apply AM-GM inequality?

Published on 11 Feb 2017 - 19:26

238

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How prove this inequality with $a+b+c+2=abc$

Published on 25 Mar 2026 - 17:19

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Given the positive numbers $a, b, c$. Prove that $\frac{a}{\sqrt{a^2+1}}+\frac{b}{\sqrt{b^2+1}}+\frac{c}{\sqrt{c^2+1}}\le \frac{3}{2}$

Published on 26 Mar 2026 - 2:57

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Prove that $\frac{a}{\sqrt{a^2+b^2}}+\frac{b}{\sqrt{9a^2+b^2}}+\frac{2ab}{\sqrt{a^2+b^2}\times \sqrt{9a^2+b^2} }\leq \frac32.$

Published on 21 Feb 2017 - 11:30

152

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Prove the inequality, fractions.

Published on 21 Feb 2017 - 19:22

99

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Minimize $P=5\left(x^2+y^2\right)+2z^2$

Published on 22 Feb 2017 - 14:37

41

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Quadratic mean inequality where arguments are linearly combination with 1

Published on 23 Feb 2017 - 15:34

62

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Prove the following inequality using the AM-GM inequality.

Published on 23 Feb 2017 - 21:25

201

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Tricky inequality involving 3 variables

Published on 24 Feb 2017 - 10:29

207

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Let $a,b,c\in \Bbb R^+$ such that $(1+a+b+c)(1+\frac{1}{a}+\frac{1}{b}+\frac{1}{c})=16$. Find $(a+b+c)$

Published on 27 Feb 2017 - 11:24

List Question

Two inequalities involving the rearrangement inequality

values of $a$ in inequality

Finding maxima and minima of $f(x,y)= x^4 + y^4 - 2x^2 - 2y^2 + 4xy$

Proving the inequality $(a^2-ab+b^2)(c^2-ac+a^2)(b^2-bc+c^2) \le 12$.

Lower bound for $\frac{(x+y+z)^3}{xy+yz+zx}$

Which is the correct way to apply AM-GM inequality?

How prove this inequality with $a+b+c+2=abc$

Given the positive numbers $a, b, c$. Prove that $\frac{a}{\sqrt{a^2+1}}+\frac{b}{\sqrt{b^2+1}}+\frac{c}{\sqrt{c^2+1}}\le \frac{3}{2}$

Prove that $\frac{a}{\sqrt{a^2+b^2}}+\frac{b}{\sqrt{9a^2+b^2}}+\frac{2ab}{\sqrt{a^2+b^2}\times \sqrt{9a^2+b^2} }\leq \frac32.$

Prove the inequality, fractions.

Minimize $P=5\left(x^2+y^2\right)+2z^2$

Quadratic mean inequality where arguments are linearly combination with 1

Prove the following inequality using the AM-GM inequality.

Tricky inequality involving 3 variables

Let $a,b,c\in \Bbb R^+$ such that $(1+a+b+c)(1+\frac{1}{a}+\frac{1}{b}+\frac{1}{c})=16$. Find $(a+b+c)$

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