Question

Proving that $(a+b)^p + (a-b)^p \geq 2a^p + p(p-1)a^{p-2}b^2$ for $p \in [1,2]$ and $0 \leq b \leq a$

score 116 · Answer 1 · 2018-02-16 01:42:10

116

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Proving that $(a+b)^p + (a-b)^p \geq 2a^p + p(p-1)a^{p-2}b^2$ for $p \in [1,2]$ and $0 \leq b \leq a$

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score 645 · Answer 2 · 2026-03-24 22:33:07

645

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isoperimetric inequality proof

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score 48 · Answer 3 · 2018-02-16 04:43:01

48

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score 42 · Answer 4 · 2026-03-26 20:44:35

42

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37

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score 172 · Answer 6 · 2026-03-25 06:05:47

172

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Bounds for generalized mean $\frac{1}{2 \mu(a,b)}=\int_0^\infty \frac{dx}{e^{ax}+e^{bx}}$

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score 78 · Answer 7 · 2026-03-23 11:31:29

78

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score 136 · Answer 8 · 2026-03-23 02:58:17

136

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score 73 · Answer 9 · 2018-02-17 10:17:09

73

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score 60 · Answer 10 · 2018-02-17 12:40:43

60

Views

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score 52 · Answer 11 · 2026-03-25 15:45:35

52

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score 101 · Answer 12 · 2018-02-17 16:10:47

101

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score 111 · Answer 13 · 2018-02-17 18:18:43

111

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score 51 · Answer 14 · 2018-02-17 22:05:21

51

Views

Proving that $8(x+1)^3 \ge (n+1)^3(x+n)$ for $n \ge 3$ and $x \ge n^2$

Published on 17 Feb 2018 - 22:05

score 1.2k · Answer 15 · 2018-02-18 02:36:48

1.2k

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I don't understand this system of inequalities word problem

Published on 18 Feb 2018 - 2:36

List Question

Proving that $(a+b)^p + (a-b)^p \geq 2a^p + p(p-1)a^{p-2}b^2$ for $p \in [1,2]$ and $0 \leq b \leq a$

isoperimetric inequality proof

Proof related to inequalities

Proving an inequality by rearranging it

An inequality in innerproduct space

Bounds for generalized mean $\frac{1}{2 \mu(a,b)}=\int_0^\infty \frac{dx}{e^{ax}+e^{bx}}$

Proving inequality for all real $a$ and $b$.

Inequality involving power to fractional part of integer multiples of logarithm of integer to coprime base.

Show that $\frac1x+\log x-\log(x+1)\ge0$ for $x\ge1$ without differential calculus

Trigonometry inequality with 2 natural parameters.

solving linear equation with modulus

A refinement of a difficult inequality involving reciprocal gamma function

How to solve the inequality analytically?

Proving that $8(x+1)^3 \ge (n+1)^3(x+n)$ for $n \ge 3$ and $x \ge n^2$

I don't understand this system of inequalities word problem

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