Question

Proving $Q=\frac{a^{3}+b^{3}+c^{3}}{(a+b)(b+c)(c+a)}+k\cdot \frac{(ab+bc+ca)}{(a+b+c)^{2}}\geqslant \frac{3}{8}+\frac{k}{3}$

score 124 · Answer 1 · 2026-03-26 16:10:14

124

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Proving $Q=\frac{a^{3}+b^{3}+c^{3}}{(a+b)(b+c)(c+a)}+k\cdot \frac{(ab+bc+ca)}{(a+b+c)^{2}}\geqslant \frac{3}{8}+\frac{k}{3}$

Published on 26 Mar 2026 - 16:10

score 2.8k · Answer 2 · 2026-04-12 02:47:49

2.8k

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Prove that $\sqrt{8}$ is irrational in different method

Published on 12 Apr 2026 - 2:47

score 161 · Answer 3 · 2026-03-26 23:10:46

161

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Is this alternative proof of the inequality $\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\geq\frac{3}{2}$ correct?

Published on 26 Mar 2026 - 23:10

score 105 · Answer 4 · 2026-04-12 17:02:28

105

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Is there a direct way to prove that the infimum over all convex combinations is convex?

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score 1.3k · Answer 5 · 2026-04-10 14:50:29

1.3k

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How to prove column orthogonality of character table

Published on 10 Apr 2026 - 14:50

score 134 · Answer 6 · 2026-04-04 00:50:22

134

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Simpler ways of finding solutions to $\int_0^x \lfloor{x\rfloor}^2 dx=2(x-1)$

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score 238 · Answer 7 · 2026-04-13 06:21:38

238

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score 105 · Answer 8 · 2026-04-11 18:49:44

105

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score 91 · Answer 9 · 2026-04-08 16:21:06

91

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Alternative to the proof on Wolfram Mathworld that $\mathbb Q$ is the smallest subfield of $\mathbb R$

Published on 08 Apr 2026 - 16:21

score 175 · Answer 10 · 2026-03-30 00:22:48

175

Views

Prove $\sum_{m=i}^{n}2^{n-m}\binom{m}{i}=\binom{n+1}{i+1}+\ldots+\binom{n+1}{n+1}=\sum_{m=i}^{n}\binom{n+1}{m+1}$ without induction

Published on 30 Mar 2026 - 0:22

score 75 · Answer 11 · 2026-04-13 06:31:45

75

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Proving that $\sup (A + B) = \sup (A) + \sup (B)$ through two contradictions

Published on 13 Apr 2026 - 6:31

score 88 · Answer 12 · 2020-09-04 12:49:20

88

Views

If $R$ is a total order over set $A$, then all subsets of $A$ can be sorted

Published on 04 Sep 2020 - 12:49

score 97 · Answer 13 · 2020-09-04 19:21:32

97

Views

Inexistence or limit that does not exist

Published on 04 Sep 2020 - 19:21

score 243 · Answer 14 · 2026-04-12 17:24:55

243

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Number of ways to arrange the boys and girls

Published on 12 Apr 2026 - 17:24

score 45 · Answer 15 · 2026-04-10 19:57:40

45

Views

Does this method fail in proving the given inequality?

Published on 10 Apr 2026 - 19:57

List Question

Proving $Q=\frac{a^{3}+b^{3}+c^{3}}{(a+b)(b+c)(c+a)}+k\cdot \frac{(ab+bc+ca)}{(a+b+c)^{2}}\geqslant \frac{3}{8}+\frac{k}{3}$

Prove that $\sqrt{8}$ is irrational in different method

Is this alternative proof of the inequality $\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\geq\frac{3}{2}$ correct?

Is there a direct way to prove that the infimum over all convex combinations is convex?

How to prove column orthogonality of character table

Simpler ways of finding solutions to $\int_0^x \lfloor{x\rfloor}^2 dx=2(x-1)$

Proofs of the Volume of a Sphere.

Verification for a series of limits

Alternative to the proof on Wolfram Mathworld that $\mathbb Q$ is the smallest subfield of $\mathbb R$

Prove $\sum_{m=i}^{n}2^{n-m}\binom{m}{i}=\binom{n+1}{i+1}+\ldots+\binom{n+1}{n+1}=\sum_{m=i}^{n}\binom{n+1}{m+1}$ without induction

Proving that $\sup (A + B) = \sup (A) + \sup (B)$ through two contradictions

If $R$ is a total order over set $A$, then all subsets of $A$ can be sorted

Inexistence or limit that does not exist

Number of ways to arrange the boys and girls

Does this method fail in proving the given inequality?

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