Question

Inequality $\sqrt{1+x^2}+\sqrt{1+y^2}+\sqrt{1+z^2} \le \sqrt{2}(x+y+z)$

score 325 · Answer 1 · 2026-03-25 12:28:22

325

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Inequality $\sqrt{1+x^2}+\sqrt{1+y^2}+\sqrt{1+z^2} \le \sqrt{2}(x+y+z)$

Published on 25 Mar 2026 - 12:28

score 171 · Answer 2 · 2015-01-19 13:55:44

171

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Inequalites of triangle side with $abc = 1$

Published on 19 Jan 2015 - 13:55

score 195 · Answer 3 · 2015-04-18 16:49:50

195

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Inequality with condition $x+y+z=xy+yz+zx$

Published on 18 Apr 2015 - 16:49

score 4.1k · Answer 4 · 2015-04-24 14:57:05

4.1k

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Prove QM-AM inequality

Published on 24 Apr 2015 - 14:57

score 3.6k · Answer 5 · 2015-05-04 04:55:54

3.6k

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Express a quadratic form as a sum of squares using Schur complements

Published on 04 May 2015 - 4:55

score 290 · Answer 6 · 2026-03-25 12:17:20

290

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Explicit LMI representation of sum of square (SOS) cones

Published on 25 Mar 2026 - 12:17

score 794 · Answer 7 · 2015-12-29 18:52:38

794

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Prove that $\sqrt{x_1}+\sqrt{x_2}+\cdots+\sqrt{x_n} \geq (n-1) \left (\frac{1}{\sqrt{x_1}}+\frac{1}{\sqrt{x_2}}+\cdots+\frac{1}{\sqrt{x_n}} \right )$

Published on 29 Dec 2015 - 18:52

score 4k · Answer 8 · 2016-01-01 08:53:42

4k

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Prove that $a\sqrt{a^2+bc}+b\sqrt{b^2+ac}+c\sqrt{c^2+ab}\geq\sqrt{2(a^2+b^2+c^2)(ab+ac+bc)}$

Published on 01 Jan 2016 - 8:53

score 116 · Answer 9 · 2026-03-12 15:45:54

116

Views

inequality with three variables and condition

Published on 12 Mar 2026 - 15:45

score 194 · Answer 10 · 2016-01-08 11:13:03

194

Views

Prove that $\frac{bc}{a^2+bc}+\frac{ca}{b^2+ca}+\frac{ab}{c^2+ab}\le{\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b}}$

Published on 08 Jan 2016 - 11:13

score 242 · Answer 11 · 2016-01-19 01:07:39

242

Views

Prove that $m_a(bc-a^2)+m_b(ac-b^2)+m_c(ab-c^2) \geq 0.$

Published on 19 Jan 2016 - 1:07

score 2k · Answer 12 · 2016-01-26 15:33:30

2k

Views

Prove that $\frac{a}{b+2c+3d}+\frac{b}{c+2d+3a}+\frac{c}{d+2a+3b}+\frac{d}{a+2b+3c} \geq \frac{2}{3}.$

Published on 26 Jan 2016 - 15:33

score 158 · Answer 13 · 2016-04-07 04:47:46

158

Views

Question about an inequality which seems right but not easy to prove

Published on 07 Apr 2016 - 4:47

score 82 · Answer 14 · 2016-05-09 00:39:51

82

Views

prove that $(ab+bc+ca)\bigg(\frac{a}{b(a^2+2b^2)}+\frac{b}{c(b^2+2c^2)}+\frac{c}{a(c^2+2a^2)}\bigg) \ge 3$

Published on 09 May 2016 - 0:39

score 167 · Answer 15 · 2016-05-22 04:55:00

167

Views

Show that $(a + b)^4 + (a + c)^4 + (a + d)^4 + (b + c)^4 + (b + d)^4 + (c + d)^4 \le 6$ for $a^2 + b^2 + c^2 + d^2 = 1$.

Published on 22 May 2016 - 4:55

List Question

Inequality $\sqrt{1+x^2}+\sqrt{1+y^2}+\sqrt{1+z^2} \le \sqrt{2}(x+y+z)$

Inequalites of triangle side with $abc = 1$

Inequality with condition $x+y+z=xy+yz+zx$

Prove QM-AM inequality

Express a quadratic form as a sum of squares using Schur complements

Explicit LMI representation of sum of square (SOS) cones

Prove that $\sqrt{x_1}+\sqrt{x_2}+\cdots+\sqrt{x_n} \geq (n-1) \left (\frac{1}{\sqrt{x_1}}+\frac{1}{\sqrt{x_2}}+\cdots+\frac{1}{\sqrt{x_n}} \right )$

Prove that $a\sqrt{a^2+bc}+b\sqrt{b^2+ac}+c\sqrt{c^2+ab}\geq\sqrt{2(a^2+b^2+c^2)(ab+ac+bc)}$

inequality with three variables and condition

Prove that $\frac{bc}{a^2+bc}+\frac{ca}{b^2+ca}+\frac{ab}{c^2+ab}\le{\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b}}$

Prove that $m_a(bc-a^2)+m_b(ac-b^2)+m_c(ab-c^2) \geq 0.$

Prove that $\frac{a}{b+2c+3d}+\frac{b}{c+2d+3a}+\frac{c}{d+2a+3b}+\frac{d}{a+2b+3c} \geq \frac{2}{3}.$

Question about an inequality which seems right but not easy to prove

prove that $(ab+bc+ca)\bigg(\frac{a}{b(a^2+2b^2)}+\frac{b}{c(b^2+2c^2)}+\frac{c}{a(c^2+2a^2)}\bigg) \ge 3$

Show that $(a + b)^4 + (a + c)^4 + (a + d)^4 + (b + c)^4 + (b + d)^4 + (c + d)^4 \le 6$ for $a^2 + b^2 + c^2 + d^2 = 1$.

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