Question

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

score 194 · Answer 1 · 2026-03-25 03:22:14

194

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 25 Mar 2026 - 3:22

score 101 · Answer 2 · 2019-08-10 13:16:44

101

Views

Find the number of possible partitions.

Published on 10 Aug 2019 - 13:16

score 238 · Answer 3 · 2019-08-10 13:58:13

238

Views

4 distinct integers with prime sum for each triple

Published on 10 Aug 2019 - 13:58

score 1.5k · Answer 4 · 2019-08-11 09:12:55

1.5k

Views

No.of pairs of parallel diagonals

Published on 11 Aug 2019 - 9:12

score 166 · Answer 5 · 2026-03-27 16:26:12

166

Views

Inequalities: BMO 2009/10 Round 2

Published on 27 Mar 2026 - 16:26

score 600 · Answer 6 · 2019-08-12 04:59:29

600

Views

$f_1(k)=$ square of sum of digits of $k$; $f_n(k)=f_1(f_{n-1}(k))$; find $f_{1988}(11)$

Published on 12 Aug 2019 - 4:59

score 49 · Answer 7 · 2026-03-25 07:43:33

49

Views

An inequality with sides of a triangle

Published on 25 Mar 2026 - 7:43

score 79 · Answer 8 · 2019-08-12 15:34:35

79

Views

Integration of $\frac{1}{1-\cos(\alpha)\cos x }$

Published on 12 Aug 2019 - 15:34

score 105 · Answer 9 · 2026-03-29 03:36:58

105

Views

How many solution are there to the equation $n_1^4+n_2^4+...+n_{16}^4=65536$ with non-negative integers

Published on 29 Mar 2026 - 3:36

score 81 · Answer 10 · 2026-03-29 03:35:59

81

Views

Determine all positive integer solution sets $(k, n, l, m)$ to the equation $(1 + n^k)^l=1+n^m$ where $l>1$

Published on 29 Mar 2026 - 3:35

score 131 · Answer 11 · 2019-08-13 05:55:07

131

Views

Given $x, y$ that $xy-\frac{x}{y^2}-\frac{y}{x^2}=3$, work out $xy-x-y$.

Published on 13 Aug 2019 - 5:55

score 78 · Answer 12 · 2026-03-25 09:50:17

78

Views

Prove $(x^{3} + x^{4} +y^{3} + y^{4} + z^{3} + z^{4})^{2} \le (x^{6} + y^{6} + z^{6})[ (1+x)^{2} + (1+y)^{2} + (1+z)^{2} ] $

Published on 25 Mar 2026 - 9:50

score 52 · Answer 13 · 2026-03-25 09:51:16

52

Views

Prove $ (x^{3} + x^{4} +y^{3} + y^{4} + z^{3} + z^{4})^{3} \le (x^{9} + y^{9} + z^{9})[ (1+x)^{3/2} + (1+y)^{3/2} + (1+z)^{3/2} ]^{2} $

Published on 25 Mar 2026 - 9:51

score 88 · Answer 14 · 2026-03-28 04:01:52

88

Views

Redux: An interesting four sum inequality (feat. probability)

Published on 28 Mar 2026 - 4:01

score 337 · Answer 15 · 2026-03-20 17:19:07

337

Views

For positive $a$, $b$, $c$ with $abc=1$, show that $\sum_{cyc}\sqrt{a^2-a+1}\geq a+b+c$

Published on 20 Mar 2026 - 17:19

List Question

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

Find the number of possible partitions.

4 distinct integers with prime sum for each triple

No.of pairs of parallel diagonals

Inequalities: BMO 2009/10 Round 2

$f_1(k)=$ square of sum of digits of $k$; $f_n(k)=f_1(f_{n-1}(k))$; find $f_{1988}(11)$

An inequality with sides of a triangle

Integration of $\frac{1}{1-\cos(\alpha)\cos x }$

How many solution are there to the equation $n_1^4+n_2^4+...+n_{16}^4=65536$ with non-negative integers

Determine all positive integer solution sets $(k, n, l, m)$ to the equation $(1 + n^k)^l=1+n^m$ where $l>1$

Given $x, y$ that $xy-\frac{x}{y^2}-\frac{y}{x^2}=3$, work out $xy-x-y$.

Prove $(x^{3} + x^{4} +y^{3} + y^{4} + z^{3} + z^{4})^{2} \le (x^{6} + y^{6} + z^{6})[ (1+x)^{2} + (1+y)^{2} + (1+z)^{2} ] $

Prove $ (x^{3} + x^{4} +y^{3} + y^{4} + z^{3} + z^{4})^{3} \le (x^{9} + y^{9} + z^{9})[ (1+x)^{3/2} + (1+y)^{3/2} + (1+z)^{3/2} ]^{2} $

Redux: An interesting four sum inequality (feat. probability)

For positive $a$, $b$, $c$ with $abc=1$, show that $\sum_{cyc}\sqrt{a^2-a+1}\geq a+b+c$

Trending Questions

Popular # Hahtags

Popular Questions