List questions from inequality

Published on 13 Apr 2026 - 0:01

379

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Prove that $({a\over a+b})^3+({b\over b+c})^3+ ({c\over c+a})^3\geq {3\over 8}$

Published on 25 Mar 2026 - 3:21

1.3k

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Given that $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=1$.Show that:$(a+1)(b+1)(c+1)\ge 64$

Published on 25 Mar 2026 - 1:18

41

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A problem about three sequences.

Published on 12 Apr 2026 - 0:37

591

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Prove that $(1-x)^n \leq 1 -xn+\frac{n(n-1)}{2}x^2$ when $0\leq x\leq 1$ and $n\geq2$

Published on 26 Mar 2026 - 6:32

124

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Solve for the exponent of a matrix

Published on 28 Mar 2026 - 5:28

22

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Proving inequality relation between two complex numbers and a positive real parameter.

Published on 11 Apr 2026 - 13:12

240

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Show $\sqrt{x (1-y)} - \sqrt{y (1-x)} + y\sqrt{x} - x\sqrt{y} - \frac{x - y}{3} > 0$

Published on 05 Dec 2018 - 18:46

52

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Double inequality with a certain number of reals

Published on 05 Dec 2018 - 19:57

903

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Find Chebyshev's upper bound for this probability

Published on 05 Dec 2018 - 21:17

68

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Proof of an inequality: is it correct?

Published on 27 Mar 2026 - 10:58

462

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How to find the domain of a log function?

Published on 12 Apr 2026 - 6:34

1.9k

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For sufficiently large $n$, Which number is bigger, $2^n$ or $n^{1000}$?

Published on 29 Mar 2026 - 8:44

86

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Cleverly finding the minimum of function

Published on 11 Apr 2026 - 6:48

161

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Application of weighted AM-GM

Published on 10 Apr 2026 - 5:27

List Question

Where does one even need Bernoulli's Inequality?

Prove that $({a\over a+b})^3+({b\over b+c})^3+ ({c\over c+a})^3\geq {3\over 8}$

Given that $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=1$.Show that:$(a+1)(b+1)(c+1)\ge 64$

A problem about three sequences.

Prove that $(1-x)^n \leq 1 -xn+\frac{n(n-1)}{2}x^2$ when $0\leq x\leq 1$ and $n\geq2$

Solve for the exponent of a matrix

Proving inequality relation between two complex numbers and a positive real parameter.

Show $\sqrt{x (1-y)} - \sqrt{y (1-x)} + y\sqrt{x} - x\sqrt{y} - \frac{x - y}{3} > 0$

Double inequality with a certain number of reals

Find Chebyshev's upper bound for this probability

Proof of an inequality: is it correct?

How to find the domain of a log function?

For sufficiently large $n$, Which number is bigger, $2^n$ or $n^{1000}$?

Cleverly finding the minimum of function

Application of weighted AM-GM

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