Question

Prove that $(x + y + z)^3 + 9xyz \ge 4(x + y + z)(xy + yz + zx)$ where $x, y, z \ge 0$.

score 223 · Answer 1 · 2026-03-26 02:56:22

223

Views

Prove that $(x + y + z)^3 + 9xyz \ge 4(x + y + z)(xy + yz + zx)$ where $x, y, z \ge 0$.

Published on 26 Mar 2026 - 2:56

score 3.7k · Answer 2 · 2019-06-08 06:20:51

3.7k

Views

Circular Permutations. Difference between clockwise and anti-clockwise permutations.

Published on 08 Jun 2019 - 6:20

score 67 · Answer 3 · 2026-03-26 04:34:20

67

Views

Prove that $x_1 + x_2 = y_1 + y_2 = z_1 + z_2$.

Published on 26 Mar 2026 - 4:34

score 171 · Answer 4 · 2026-03-26 20:18:50

171

Views

Nice olympiad inequality

Published on 26 Mar 2026 - 20:18

score 806 · Answer 5 · 2019-06-08 14:47:56

806

Views

shortest distance in triangle

Published on 08 Jun 2019 - 14:47

score 95 · Answer 6 · 2026-03-27 04:58:54

95

Views

Given $ a_{k+1} \ge \frac{k a_{k}}{(a_{k}^{2} + k-1)}, \:\: k > 0$, prove $ S_{n} = a_{1} + .. + a_{n} \ge n, \:\: n \ge 2 $

Published on 27 Mar 2026 - 4:58

score 529 · Answer 7 · 2019-06-09 03:26:28

529

Views

Putnam Combinatorics/Set Theory Question

Published on 09 Jun 2019 - 3:26

score 82 · Answer 8 · 2026-03-29 18:30:31

82

Views

Proving results on quadratic equations

Published on 29 Mar 2026 - 18:30

score 831 · Answer 9 · 2026-03-28 12:13:32

831

Views

Solve for integer $m,n$: $2^m = 3^n + 5$

Published on 28 Mar 2026 - 12:13

score 90 · Answer 10 · 2026-03-28 14:00:22

90

Views

Alternative Solutions to “American Billions” like puzzles: Find a 9-digit number (no repeats), where the first digits give a number divisible by

Published on 28 Mar 2026 - 14:00

score 813 · Answer 11 · 2026-03-28 12:14:05

813

Views

Prove that $6|a+b+c $ if and only if $6|a^3 +b^3+c^3$

Published on 28 Mar 2026 - 12:14

score 49 · Answer 12 · 2026-03-27 18:48:44

49

Views

Series answer for larger constraints

Published on 27 Mar 2026 - 18:48

score 360 · Answer 13 · 2026-03-28 15:11:53

360

Views

How can I find all solutions of this equation?

Published on 28 Mar 2026 - 15:11

score 127 · Answer 14 · 2026-03-26 20:16:42

127

Views

Calculate the maximum value of $\sqrt{\frac{3yz}{3yz + x}} + \sqrt{\frac{3zx}{3zx + 4y}} + \sqrt{\frac{xy}{xy + 3z}}$ where $x + 2y + 3z = 2$

Published on 26 Mar 2026 - 20:16

score 151 · Answer 15 · 2019-06-11 07:57:22

151

Views

$ \sum_{1 \le i < j \le n} a_{i} a_{j} \ge n(n-1)/2 $ , prove that $a_{1} + ... + a_{n} \ge n$ for $n \ge 2$ using AM-QM

Published on 11 Jun 2019 - 7:57

List Question

Prove that $(x + y + z)^3 + 9xyz \ge 4(x + y + z)(xy + yz + zx)$ where $x, y, z \ge 0$.

Circular Permutations. Difference between clockwise and anti-clockwise permutations.

Prove that $x_1 + x_2 = y_1 + y_2 = z_1 + z_2$.

Nice olympiad inequality

shortest distance in triangle

Given $ a_{k+1} \ge \frac{k a_{k}}{(a_{k}^{2} + k-1)}, \:\: k > 0$, prove $ S_{n} = a_{1} + .. + a_{n} \ge n, \:\: n \ge 2 $

Putnam Combinatorics/Set Theory Question

Proving results on quadratic equations

Solve for integer $m,n$: $2^m = 3^n + 5$

Alternative Solutions to “American Billions” like puzzles: Find a 9-digit number (no repeats), where the first digits give a number divisible by

Prove that $6|a+b+c $ if and only if $6|a^3 +b^3+c^3$

Series answer for larger constraints

How can I find all solutions of this equation?

Calculate the maximum value of $\sqrt{\frac{3yz}{3yz + x}} + \sqrt{\frac{3zx}{3zx + 4y}} + \sqrt{\frac{xy}{xy + 3z}}$ where $x + 2y + 3z = 2$

$ \sum_{1 \le i < j \le n} a_{i} a_{j} \ge n(n-1)/2 $ , prove that $a_{1} + ... + a_{n} \ge n$ for $n \ge 2$ using AM-QM

Trending Questions

Popular # Hahtags

Popular Questions