Question

Find the maximum value of $x^3 + y^3 + z^3$ where $x, y, z \in [0, 2]$ and $x + y + z = 3$.

score 154 · Answer 1 · 2019-06-17 09:57:48

154

Views

Find the maximum value of $x^3 + y^3 + z^3$ where $x, y, z \in [0, 2]$ and $x + y + z = 3$.

Published on 17 Jun 2019 - 9:57

score 152 · Answer 2 · 2019-06-27 03:53:58

152

Views

Number of real roots of $3^x+4^x=2^x+5^x$ with proof

Published on 27 Jun 2019 - 3:53

score 140 · Answer 3 · 2019-07-05 11:59:52

140

Views

Stronger than Jensen's inequality

Published on 05 Jul 2019 - 11:59

score 67 · Answer 4 · 2019-07-25 17:43:01

67

Views

Without majorization how to prove this inequality?

Published on 25 Jul 2019 - 17:43

score 48 · Answer 5 · 2019-07-27 12:34:09

48

Views

Is there a way to prove the next inequality without using the binomial series?

Published on 27 Jul 2019 - 12:34

score 409 · Answer 6 · 2019-08-05 16:57:11

409

Views

Upper Bound for a Sum

Published on 05 Aug 2019 - 16:57

score 76 · Answer 7 · 2019-08-08 12:43:04

76

Views

Prove that $(\sum_{i=1}^m (x_{i})^{p})^{q}\ge(\sum_{i=1}^m(x_{i})^{q})^{p}$ for all $x_i\in\mathbb R^+$ and $p,q\in\mathbb R^+$ such that $p \le q$

Published on 08 Aug 2019 - 12:43

score 193 · Answer 8 · 2019-08-10 12:33:51

193

Views

Inequality $\frac{\ln(7a+b)}{7a+b}+\frac{\ln(7b+c)}{7b+c}+\frac{\ln(7c+a)}{7c+a}\leq \frac{3\ln(8\sqrt{3})}{8\sqrt{3}}$

Published on 10 Aug 2019 - 12:33

score 118 · Answer 9 · 2019-08-12 13:44:59

118

Views

Range of function $f(x)=\sqrt{4-x^2}+\sqrt{x^2-1}$

Published on 12 Aug 2019 - 13:44

score 935 · Answer 10 · 2019-08-30 03:40:51

935

Views

Minimum and maximum sum of squares given constraints

Published on 30 Aug 2019 - 3:40

score 147 · Answer 11 · 2019-09-20 17:27:59

147

Views

Prove that $\sqrt{x^{3} + y^{3}+1} + \sqrt{z^{3} + y^{3}+1} + \sqrt{x^{3} + z^{3}+1} \ge 2 + \sqrt{2(x^{3} + y^{3}+z^{3})+1}$

Published on 20 Sep 2019 - 17:27

score 122 · Answer 12 · 2019-09-23 08:29:01

122

Views

Given three non-negative numbers $x,y,z$ so that $x+y+z=100$ and $x,y,z\notin (\!33,34\!)$. Prove that $xyz\leqq 33\cdot 34\cdot 33$ .

Published on 23 Sep 2019 - 8:29

score 173 · Answer 13 · 2014-04-10 22:15:04

173

Views

Prove that positive $x,y,z$ satisfy $\sqrt{x+y}+\sqrt{y+z}+\sqrt{z+x}\ge \sqrt{2x}+\sqrt{2y}+\sqrt{2z}$

Published on 10 Apr 2014 - 22:15

score 39 · Answer 14 · 2019-10-30 18:53:38

39

Views

Inequality with variable expoent

Published on 30 Oct 2019 - 18:53

score 102 · Answer 15 · 2020-01-02 16:57:00

102

Views

Prove that $\sum_{i=1}^n\frac{\sum_{i'=1}^na_{i'}^p - a_i^p}{\sum_{i'=1}^na_{i'}^q - a_i^q}\le n\cdot\frac{\sum_{i=1}^na_i^p}{\sum_{i=1}^na_i^q}$.

Published on 02 Jan 2020 - 16:57

List Question

Find the maximum value of $x^3 + y^3 + z^3$ where $x, y, z \in [0, 2]$ and $x + y + z = 3$.

Number of real roots of $3^x+4^x=2^x+5^x$ with proof

Stronger than Jensen's inequality

Without majorization how to prove this inequality?

Is there a way to prove the next inequality without using the binomial series?

Upper Bound for a Sum

Prove that $(\sum_{i=1}^m (x_{i})^{p})^{q}\ge(\sum_{i=1}^m(x_{i})^{q})^{p}$ for all $x_i\in\mathbb R^+$ and $p,q\in\mathbb R^+$ such that $p \le q$

Inequality $\frac{\ln(7a+b)}{7a+b}+\frac{\ln(7b+c)}{7b+c}+\frac{\ln(7c+a)}{7c+a}\leq \frac{3\ln(8\sqrt{3})}{8\sqrt{3}}$

Range of function $f(x)=\sqrt{4-x^2}+\sqrt{x^2-1}$

Minimum and maximum sum of squares given constraints

Prove that $\sqrt{x^{3} + y^{3}+1} + \sqrt{z^{3} + y^{3}+1} + \sqrt{x^{3} + z^{3}+1} \ge 2 + \sqrt{2(x^{3} + y^{3}+z^{3})+1}$

Given three non-negative numbers $x,y,z$ so that $x+y+z=100$ and $x,y,z\notin (\!33,34\!)$. Prove that $xyz\leqq 33\cdot 34\cdot 33$ .

Prove that positive $x,y,z$ satisfy $\sqrt{x+y}+\sqrt{y+z}+\sqrt{z+x}\ge \sqrt{2x}+\sqrt{2y}+\sqrt{2z}$

Inequality with variable expoent

Prove that $\sum_{i=1}^n\frac{\sum_{i'=1}^na_{i'}^p - a_i^p}{\sum_{i'=1}^na_{i'}^q - a_i^q}\le n\cdot\frac{\sum_{i=1}^na_i^p}{\sum_{i=1}^na_i^q}$.

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