Question

An inequality with sides of a triangle

score 50 · Answer 1 · 2026-04-01 09:41:18

50

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An inequality with sides of a triangle

Published on 01 Apr 2026 - 9:41

score 293 · Answer 2 · 2026-03-25 07:44:36

293

Views

How prove $\frac{a}{11a+9b+c}+\frac{b}{11b+9c+a}+\frac{c}{11c+9a+b}\le\frac{1}{7}$

Published on 25 Mar 2026 - 7:44

score 970 · Answer 3 · 2026-03-25 07:44:45

970

Views

Prove $\frac{a}{a+bc}+\frac{b}{b+cd}+\frac{c}{c+da}+\frac{d}{d+ab}\ge 2$ for positives $\sum a = 4$

Published on 25 Mar 2026 - 7:44

score 334 · Answer 4 · 2026-03-25 07:44:49

334

Views

For $x+y+z=3$ prove that $4\geqq x^2y+y^2z+z^2x$

Published on 25 Mar 2026 - 7:44

score 237 · Answer 5 · 2026-03-25 07:46:29

237

Views

How prove this Nice inequality $\sum\limits_\text{cyc}\frac{x^2}{y}\ge 3+\frac{x^4+y^4+z^4-x^2-y^2-z^2}{x^3+y^3+z^3-xyz}$

Published on 25 Mar 2026 - 7:46

score 1k · Answer 6 · 2026-03-25 07:45:30

1k

Views

For any triangle with sides $a$, $b$, $c$, show that $a^2b(a-b)+b^2c(b-c)+c^2a(c-a)\ge 0$

Published on 25 Mar 2026 - 7:45

score 191 · Answer 7 · 2026-04-27 20:48:08

191

Views

Proving a much stronger version of AM-GM for three variables

Published on 27 Apr 2026 - 20:48

score 503 · Answer 8 · 2026-04-14 13:36:18

503

Views

Inequality in 4 variables Vasc's EV

Published on 14 Apr 2026 - 13:36

score 93 · Answer 9 · 2026-04-13 01:26:50

93

Views

Proving an interesting inequality with square roots

Published on 13 Apr 2026 - 1:26

score 731 · Answer 10 · 2026-04-29 15:10:40

731

Views

If $x,y,z>0.$Prove: $(x+y+z) \left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z} \right) \geq9\sqrt[]\frac{x^2+y^2+z^2}{xy+yz+zx}$

Published on 29 Apr 2026 - 15:10

score 307 · Answer 11 · 2020-01-09 19:04:26

307

Views

Find $\max(x^2y+y^2z+z^2x+xyz)(x^2z+y^2x+z^2y+xyz)$ subject to $x+2y+3z=4$

Published on 09 Jan 2020 - 19:04

score 159 · Answer 12 · 2026-04-25 17:52:15

159

Views

An olympiad-like inequality $\frac{x^5}{6x^4+5y^4}+\frac{y^5}{6y^4+5z^4}+\frac{z^5}{6z^4+5x^4}\geq \frac{x+y+z}{11}$

Published on 25 Apr 2026 - 17:52

score 88 · Answer 13 · 2020-01-15 23:30:23

88

Views

How to prove $a^3+b^3+c^3+d^3+3\left(a+b+c+d\right) \geq 14+2abcd$ when $a^2+b^2+c^2+d^2=4$

Published on 15 Jan 2020 - 23:30

score 702 · Answer 14 · 2020-01-22 22:00:35

702

Views

Asymmetric inequality in three variables $\frac{3(a+b)^2(b+c)^2}{4ab^2c} \geq 7+\frac{5(a^2+2b^2+c^2)}{(a+b)(b+c)}$

Published on 22 Jan 2020 - 22:00

score 386 · Answer 15 · 2020-01-29 01:10:43

386

Views

$3\geq\sum\limits_{cyc}\frac{(x+y)^{2}x^{2}}{(x^{2}+y^{2})^{2}}$ with $x,y,z >0$

Published on 29 Jan 2020 - 1:10

List Question

An inequality with sides of a triangle

How prove $\frac{a}{11a+9b+c}+\frac{b}{11b+9c+a}+\frac{c}{11c+9a+b}\le\frac{1}{7}$

Prove $\frac{a}{a+bc}+\frac{b}{b+cd}+\frac{c}{c+da}+\frac{d}{d+ab}\ge 2$ for positives $\sum a = 4$

For $x+y+z=3$ prove that $4\geqq x^2y+y^2z+z^2x$

How prove this Nice inequality $\sum\limits_\text{cyc}\frac{x^2}{y}\ge 3+\frac{x^4+y^4+z^4-x^2-y^2-z^2}{x^3+y^3+z^3-xyz}$

For any triangle with sides $a$, $b$, $c$, show that $a^2b(a-b)+b^2c(b-c)+c^2a(c-a)\ge 0$

Proving a much stronger version of AM-GM for three variables

Inequality in 4 variables Vasc's EV

Proving an interesting inequality with square roots

If $x,y,z>0.$Prove: $(x+y+z) \left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z} \right) \geq9\sqrt[]\frac{x^2+y^2+z^2}{xy+yz+zx}$

Find $\max(x^2y+y^2z+z^2x+xyz)(x^2z+y^2x+z^2y+xyz)$ subject to $x+2y+3z=4$

An olympiad-like inequality $\frac{x^5}{6x^4+5y^4}+\frac{y^5}{6y^4+5z^4}+\frac{z^5}{6z^4+5x^4}\geq \frac{x+y+z}{11}$

How to prove $a^3+b^3+c^3+d^3+3\left(a+b+c+d\right) \geq 14+2abcd$ when $a^2+b^2+c^2+d^2=4$

Asymmetric inequality in three variables $\frac{3(a+b)^2(b+c)^2}{4ab^2c} \geq 7+\frac{5(a^2+2b^2+c^2)}{(a+b)(b+c)}$

$3\geq\sum\limits_{cyc}\frac{(x+y)^{2}x^{2}}{(x^{2}+y^{2})^{2}}$ with $x,y,z >0$

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