Question

prove this inequality $(x+y-z)(y+z-x)(x+z-y)(x+y+z)^3\le27 (xyz)^2$

score 526 · Answer 1 · 2026-03-25 12:51:02

526

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prove this inequality $(x+y-z)(y+z-x)(x+z-y)(x+y+z)^3\le27 (xyz)^2$

Published on 25 Mar 2026 - 12:51

score 43 · Answer 2 · 2018-07-16 16:53:10

43

Views

Restriction of interval while proving an inequality

Published on 16 Jul 2018 - 16:53

score 103 · Answer 3 · 2026-03-26 01:00:10

103

Views

An inequality with substitution

Published on 26 Mar 2026 - 1:00

score 209 · Answer 4 · 2026-03-25 11:08:51

209

Views

Eigenvalues of element-wise ordered matrices

Published on 25 Mar 2026 - 11:08

score 179 · Answer 5 · 2026-03-25 23:37:47

179

Views

Prove: $\log_2(x)+\log_x(y)+\log_y(8)\geq \sqrt[3]{81}$

Published on 25 Mar 2026 - 23:37

score 581 · Answer 6 · 2018-07-16 20:21:35

581

Views

Proof of the inequality $||a+b|^p - |a|^p| \leq \epsilon |a|^p + C_{\epsilon} |b|^p$

Published on 16 Jul 2018 - 20:21

score 144 · Answer 7 · 2026-03-25 15:37:50

144

Views

Expectation inequality for sampling without replacement

Published on 25 Mar 2026 - 15:37

score 1.1k · Answer 8 · 2026-03-25 15:43:47

1.1k

Views

The convolution of functions in the Schwartz Space lies in the Schwartz Space

Published on 25 Mar 2026 - 15:43

score 47 · Answer 9 · 2018-07-17 11:57:18

47

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Knowing that $9a^2+8ab+7b^2 \le 6$, prove that $7a+5b+12ab \le 9$.

Published on 17 Jul 2018 - 11:57

score 122 · Answer 10 · 2018-07-17 12:20:24

122

Views

If $abc=1$, prove that $\frac{2}{(a+1)^2+b^2+1} + \frac{2}{(b+1)^2+c^2+1} + \frac{2}{(c+1)^2+a^2+1} \le 1$.

Published on 17 Jul 2018 - 12:20

score 68 · Answer 11 · 2026-03-27 14:49:22

68

Views

One particular probabilistic inequality

Published on 27 Mar 2026 - 14:49

score 171 · Answer 12 · 2026-03-26 01:23:43

171

Views

Show $\frac{1}{b+c+d} + \frac{1}{a+c+d} + \frac{1}{a+b+d} + \frac{1}{a+b+c} \ge \frac{16}{3(a+b+c+d)}$.

Published on 26 Mar 2026 - 1:23

score 147 · Answer 13 · 2018-07-18 01:32:19

147

Views

Jensen Inequality - without calculus please

Published on 18 Jul 2018 - 1:32

score 76 · Answer 14 · 2026-03-27 01:47:51

76

Views

Is it true that $\sqrt{(a_1+b_1+c_1)(a_2+b_2+c_2)}\geq \sqrt{a_1a_2}+\sqrt{b_1b_2}+\sqrt{c_1c_2}$?

Published on 27 Mar 2026 - 1:47

score 120 · Answer 15 · 2026-03-31 07:47:50

120

Views

Proving roots are imaginary.

Published on 31 Mar 2026 - 7:47

List Question

prove this inequality $(x+y-z)(y+z-x)(x+z-y)(x+y+z)^3\le27 (xyz)^2$

Restriction of interval while proving an inequality

An inequality with substitution

Eigenvalues of element-wise ordered matrices

Prove: $\log_2(x)+\log_x(y)+\log_y(8)\geq \sqrt[3]{81}$

Proof of the inequality $||a+b|^p - |a|^p| \leq \epsilon |a|^p + C_{\epsilon} |b|^p$

Expectation inequality for sampling without replacement

The convolution of functions in the Schwartz Space lies in the Schwartz Space

Knowing that $9a^2+8ab+7b^2 \le 6$, prove that $7a+5b+12ab \le 9$.

If $abc=1$, prove that $\frac{2}{(a+1)^2+b^2+1} + \frac{2}{(b+1)^2+c^2+1} + \frac{2}{(c+1)^2+a^2+1} \le 1$.

One particular probabilistic inequality

Show $\frac{1}{b+c+d} + \frac{1}{a+c+d} + \frac{1}{a+b+d} + \frac{1}{a+b+c} \ge \frac{16}{3(a+b+c+d)}$.

Jensen Inequality - without calculus please

Is it true that $\sqrt{(a_1+b_1+c_1)(a_2+b_2+c_2)}\geq \sqrt{a_1a_2}+\sqrt{b_1b_2}+\sqrt{c_1c_2}$?

Proving roots are imaginary.

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