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

Published on 02 Jul 2017 - 3:56

665

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$HM-GM-AM$ inequality using Lagrange multipliers

Published on 03 Jul 2017 - 14:17

103

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Solving an inequality with AM-GM

Published on 04 Jul 2017 - 8:28

399

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Prove the inequality using AM-GM only.

Published on 05 Jul 2017 - 14:39

126

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Find the minimize value of $A=\frac{1}{\sqrt{a^2+b^2+c^2+1}}-\frac{2}{(a+1)(b+1)(c+1)}$

Published on 10 Jul 2017 - 4:01

128

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$\frac{a^3}{b^2}+\frac{b^3}{c^2}+\frac{c^3}{a^2}\geq a^2+b^2+c^2$

Published on 10 Jul 2017 - 7:57

87

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$a,b,c$ real, summing to two and multiplying to four; find minimum of $|a|+|b|+|c|$

Published on 11 Jul 2017 - 4:47

148

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Prove inequality $\sum _{cyc}\frac{2ab}{\sqrt{c+3}}\le 3$

Published on 26 Mar 2026 - 12:40

532

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Proving $a^{-2}bcd+b^{-2}cda+c^{-2}dab+d^{-2}abc\geqslant a+b+c+d$

Published on 25 Mar 2026 - 17:37

176

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Prove that inequality $\sum_{cyc} \frac{a}{b+2}\le 1$

Published on 25 Mar 2026 - 20:19

164

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Find the maximum and minimum value of $S= \log_{2}a+\log_{2}b+\log_{2}c$.

Published on 13 Jul 2017 - 16:37

88

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Minimum value problem without derivative

Published on 28 Mar 2026 - 13:29

984

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How to show Young's inequality without using concavity of the logarithm?

Published on 14 Jul 2017 - 19:39

103

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prove $\sum_{cyc}\frac{1}{a(a+b)}\ge\frac{4}{ac+bd}$

Published on 15 Jul 2017 - 4:58

2.7k

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Maximising $f(x,y)=xy^2$ subject to $x^2+y^2 = 1$ using the Lagrange Multiplier

Published on 15 Jul 2017 - 17:55

List Question

Find the largest constant $k$ such that $\frac{kabc}{a+b+c}\leq(a+b)^2+(a+b+4c)^2$

$HM-GM-AM$ inequality using Lagrange multipliers

Solving an inequality with AM-GM

Prove the inequality using AM-GM only.

Find the minimize value of $A=\frac{1}{\sqrt{a^2+b^2+c^2+1}}-\frac{2}{(a+1)(b+1)(c+1)}$

$\frac{a^3}{b^2}+\frac{b^3}{c^2}+\frac{c^3}{a^2}\geq a^2+b^2+c^2$

$a,b,c$ real, summing to two and multiplying to four; find minimum of $|a|+|b|+|c|$

Prove inequality $\sum _{cyc}\frac{2ab}{\sqrt{c+3}}\le 3$

Proving $a^{-2}bcd+b^{-2}cda+c^{-2}dab+d^{-2}abc\geqslant a+b+c+d$

Prove that inequality $\sum_{cyc} \frac{a}{b+2}\le 1$

Find the maximum and minimum value of $S= \log_{2}a+\log_{2}b+\log_{2}c$.

Minimum value problem without derivative

How to show Young's inequality without using concavity of the logarithm?

prove $\sum_{cyc}\frac{1}{a(a+b)}\ge\frac{4}{ac+bd}$

Maximising $f(x,y)=xy^2$ subject to $x^2+y^2 = 1$ using the Lagrange Multiplier

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