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

Published on 26 Jul 2018 - 13:26

138

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Show $\prod_{i=1}^{n}x_i^{\alpha_i} \leq \sum_{i=1}^{n}\alpha_ix_i$ using convexity.

Published on 28 Jul 2018 - 18:37

207

Views

Minimum value of $\frac{x^4+5x^2+7}{x^2+3}$

Published on 31 Jul 2018 - 9:25

53

Views

Find the maximum constant such that the inequality

Published on 04 Aug 2018 - 8:50

356

Views

Prove that inequality $\frac{2ab}{a+b}+\sqrt{\frac{a^2+b^2}{2}}\ge \sqrt{ab}+\frac{a+b}{2}$

Published on 05 Aug 2018 - 11:01

345

Views

Prove that $\frac{6(a^2 + b^2 + c^2)}{a + b + c} \geq \frac{(a + b)^2}{b + c} + \frac{(b + c)^2}{c + a} + \frac{(a + c)^2}{a + b}$

Published on 25 Mar 2026 - 22:05

1.6k

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Prove that: $xy\sqrt{z}+yz\sqrt{x}+zx\sqrt{y}\geq x+y+z$

Published on 25 Mar 2026 - 0:02

312

Views

Find the maximum of the value$(n^{n-1}-1)\sqrt[n]{a_{1}a_{2}\cdots a_{n}}+\sqrt[n]{\frac{a^n_{1}+a^n_{2}+\cdots+a^n_{n}}{n}}$

Published on 07 Aug 2018 - 13:29

201

Views

Prove that: $\frac{bc}{a^2+1}+\frac{ac}{b^2+1}+\frac{ab}{c^2+1}\leq \frac{3}{4}$

Published on 25 Mar 2026 - 19:06

1.5k

Views

Largest possible value of trigonometric functions

Published on 08 Aug 2018 - 8:17

557

Views

Prove that $\log_n(n+1)\geq\log_{n+1}(n+2)$ for $n>1$

Published on 08 Aug 2018 - 18:52

182

Views

How to prove AM-GM by induction 3

Published on 25 Mar 2026 - 12:48

311

Views

Generalized Sum over Product Inequality : Related to Cauchy Schwarz's and AM-GM Inequality.

Published on 12 Aug 2018 - 17:29

90

Views

Prove that $a_n \gt b_n$ $\forall $ $n \ge 6$

Published on 25 Mar 2026 - 18:56

569

Views

Inequality $\sqrt{xy+yz+zx} \ge \frac {8}{15} (x+y+z)$

Published on 25 Mar 2026 - 12:50

List Question

Finding the minimum value of $\log _d a + \log _bd + \log _ac + \log _c b$

Show $\prod_{i=1}^{n}x_i^{\alpha_i} \leq \sum_{i=1}^{n}\alpha_ix_i$ using convexity.

Minimum value of $\frac{x^4+5x^2+7}{x^2+3}$

Find the maximum constant such that the inequality

Prove that inequality $\frac{2ab}{a+b}+\sqrt{\frac{a^2+b^2}{2}}\ge \sqrt{ab}+\frac{a+b}{2}$

Prove that $\frac{6(a^2 + b^2 + c^2)}{a + b + c} \geq \frac{(a + b)^2}{b + c} + \frac{(b + c)^2}{c + a} + \frac{(a + c)^2}{a + b}$

Prove that: $xy\sqrt{z}+yz\sqrt{x}+zx\sqrt{y}\geq x+y+z$

Find the maximum of the value$(n^{n-1}-1)\sqrt[n]{a_{1}a_{2}\cdots a_{n}}+\sqrt[n]{\frac{a^n_{1}+a^n_{2}+\cdots+a^n_{n}}{n}}$

Prove that: $\frac{bc}{a^2+1}+\frac{ac}{b^2+1}+\frac{ab}{c^2+1}\leq \frac{3}{4}$

Largest possible value of trigonometric functions

Prove that $\log_n(n+1)\geq\log_{n+1}(n+2)$ for $n>1$

How to prove AM-GM by induction 3

Generalized Sum over Product Inequality : Related to Cauchy Schwarz's and AM-GM Inequality.

Prove that $a_n \gt b_n$ $\forall $ $n \ge 6$

Inequality $\sqrt{xy+yz+zx} \ge \frac {8}{15} (x+y+z)$

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