Question

Prove $\frac{a^2}{3^3}+\frac{b^2}{4^3}+\frac{c^2}{5^3} \ge \frac{(a+b+c)^2}{6^3}$

score 2.4k · Answer 1 · 2026-03-27 07:31:14

2.4k

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Prove $\frac{a^2}{3^3}+\frac{b^2}{4^3}+\frac{c^2}{5^3} \ge \frac{(a+b+c)^2}{6^3}$

Published on 27 Mar 2026 - 7:31

score 84 · Answer 2 · 2026-03-25 07:43:47

84

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Prove $\sum \frac{a}{a+b^4+c^4} \le 1$

Published on 25 Mar 2026 - 7:43

score 120 · Answer 3 · 2026-03-27 02:51:02

120

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RMO practice problem inequality

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score 462 · Answer 4 · 2026-03-25 16:01:39

462

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Convergence in Probability does not imply Convergence in Quadratic Mean: Counterexample

Published on 25 Mar 2026 - 16:01

score 35 · Answer 5 · 2018-10-06 08:55:52

35

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proof using Cauchy-Schwarz inequality 5

Published on 06 Oct 2018 - 8:55

score 183 · Answer 6 · 2026-03-26 04:51:37

183

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Find the minimum values of $a^3$ and $b^3$ from the following given cubic function.

Published on 26 Mar 2026 - 4:51

score 141 · Answer 7 · 2018-10-06 15:11:06

141

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Show the norms of $\ell_p$ and $\ell_q$ are not equivalent on the linear space $f $

Published on 06 Oct 2018 - 15:11

score 117 · Answer 8 · 2026-03-25 19:11:17

117

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A combinatorial inequality $\binom {2n}{k} + \binom {2n}{n-k} \ < \ \binom{2n}{n} + \binom{2n}{0} \ \ \text{for} \ \ k<n \ \ $

Published on 25 Mar 2026 - 19:11

score 34 · Answer 9 · 2026-04-03 11:53:08

34

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How to sort out different cases in a proof related to a metric space

Published on 03 Apr 2026 - 11:53

score 252 · Answer 10 · 2026-04-06 12:23:08

252

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Proving that $q(A,S)>0$ if $A>0$, $S<0$ and $p_i(A,S)>0$

Published on 06 Apr 2026 - 12:23

score 94 · Answer 11 · 2026-03-28 11:43:34

94

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An induction proof of $(a+1)^n (a^n+1) \leq 2^n (a^{2n}+1)$

Published on 28 Mar 2026 - 11:43

score 644 · Answer 12 · 2018-10-07 07:04:21

644

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How do I prove $2xy ≤ x^2+y^2$?

Published on 07 Oct 2018 - 7:04

score 74 · Answer 13 · 2026-03-27 15:18:14

74

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maximising function subject to the constraint without using lagrange multiplier and other calculus techqniques

Published on 27 Mar 2026 - 15:18

score 113 · Answer 14 · 2026-03-25 12:27:23

113

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Prove that $1/6 < \int_0^1 \frac{1-x^2}{3+\cos(x)}dx < 2/9$

Published on 25 Mar 2026 - 12:27

score 162 · Answer 15 · 2018-10-07 11:10:55

162

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Proving $\arctan(|x-y|)\leqslant\arctan(|x|)+\arctan(|y|)$

Published on 07 Oct 2018 - 11:10

List Question

Prove $\frac{a^2}{3^3}+\frac{b^2}{4^3}+\frac{c^2}{5^3} \ge \frac{(a+b+c)^2}{6^3}$

Prove $\sum \frac{a}{a+b^4+c^4} \le 1$

RMO practice problem inequality

Convergence in Probability does not imply Convergence in Quadratic Mean: Counterexample

proof using Cauchy-Schwarz inequality 5

Find the minimum values of $a^3$ and $b^3$ from the following given cubic function.

Show the norms of $\ell_p$ and $\ell_q$ are not equivalent on the linear space $f $

A combinatorial inequality $\binom {2n}{k} + \binom {2n}{n-k} \ < \ \binom{2n}{n} + \binom{2n}{0} \ \ \text{for} \ \ k<n \ \ $

How to sort out different cases in a proof related to a metric space

Proving that $q(A,S)>0$ if $A>0$, $S<0$ and $p_i(A,S)>0$

An induction proof of $(a+1)^n (a^n+1) \leq 2^n (a^{2n}+1)$

How do I prove $2xy ≤ x^2+y^2$?

maximising function subject to the constraint without using lagrange multiplier and other calculus techqniques

Prove that $1/6 < \int_0^1 \frac{1-x^2}{3+\cos(x)}dx < 2/9$

Proving $\arctan(|x-y|)\leqslant\arctan(|x|)+\arctan(|y|)$

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