Question

I can't find the maximum value of P because of some problems in my solution.

score 72 · Answer 1 · 2026-04-14 15:07:20

72

Views

I can't find the maximum value of P because of some problems in my solution.

Published on 14 Apr 2026 - 15:07

score 260 · Answer 2 · 2026-04-16 02:24:10

260

Views

If $a^2+b^2=1$ where $a,b>0$ then find the minimum value of $(a+b+{1\over{ab}})$

Published on 16 Apr 2026 - 2:24

score 628 · Answer 3 · 2026-04-16 09:42:45

628

Views

How to prove $\sqrt{\frac{ab}{2a^2+bc+ca}}+\sqrt{\frac{bc}{2b^2+ca+ab}}+\sqrt{\frac{ca}{2c^2+ab+bc}}\ge\frac{81}{2}\cdot\frac{abc}{(a+b+c)^3}$

Published on 16 Apr 2026 - 9:42

score 598 · Answer 4 · 2026-04-16 12:12:41

598

Views

Prove that $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\le\frac{3}{\sqrt{7}}$

Published on 16 Apr 2026 - 12:12

score 205 · Answer 5 · 2026-05-10 15:03:26

205

Views

Seeking concise proof: $\frac18(a^2+b^2)(b^2+c^2)(c^2+a^2)\ge\frac1{27}(ab+bc+ca)^3$, where $a$, $b$, $c$ are positive numbers

Published on 10 May 2026 - 15:03

score 467 · Answer 6 · 2026-04-17 11:31:57

467

Views

If the sum of cubes of $a,b,c,d$ is $1$, then $\frac{1}{1-bcd}+\frac{1}{1-cda}+\frac{1}{1-dab}+\frac{1}{1-abc}\le \frac{16}{3}$

Published on 17 Apr 2026 - 11:31

score 483 · Answer 7 · 2026-04-16 09:08:17

483

Views

Prove that $\sum\limits_{\mathrm{cyc}}{\frac{1}{(x+2y)^2}} \geq\frac{1}{xy+yz+zx}$ for $x, y, z > 0$

Published on 16 Apr 2026 - 9:08

score 1.4k · Answer 8 · 2026-04-16 17:34:19

1.4k

Views

Hard inequality $ (xy+yz+zx)\left(\frac{1}{(x+y)^2}+\frac{1}{(y+z)^2}+\frac{1}{(z+x)^2}\right)\ge\frac{9}{4} $

Published on 16 Apr 2026 - 17:34

score 930 · Answer 9 · 2026-05-07 09:52:45

930

Views

How prove this $x^3+y^3+z^3+3\ge 2(x^2+y^2+z^2)$

Published on 07 May 2026 - 9:52

score 294 · Answer 10 · 2026-04-17 08:33:05

294

Views

How prove this inequality$4(a^2+b^2+c^2)+9a^2b^2c^2\ge 21$

Published on 17 Apr 2026 - 8:33

score 190 · Answer 11 · 2026-04-16 06:10:06

190

Views

prove that $a^2 b^2 (a^2 + b^2 - 2) \ge (a + b)(ab - 1)$

Published on 16 Apr 2026 - 6:10

score 53 · Answer 12 · 2026-05-05 20:09:30

53

Views

An elegant but difficult inequality.

Published on 05 May 2026 - 20:09

score 123 · Answer 13 · 2026-05-03 21:29:53

123

Views

Finding maximum with two constraints

Published on 03 May 2026 - 21:29

score 168 · Answer 14 · 2019-11-06 01:41:12

168

Views

Prove $(\frac{x^2}{y}+\frac{y^2}{z}+\frac{z^2}{x})^3+12\ge 13(x^3+y^3+z^3)$ for positives $xyz = 1$

Published on 06 Nov 2019 - 1:41

score 732 · Answer 15 · 2026-05-10 16:13:26

732

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 10 May 2026 - 16:13

List Question

I can't find the maximum value of P because of some problems in my solution.

If $a^2+b^2=1$ where $a,b>0$ then find the minimum value of $(a+b+{1\over{ab}})$

How to prove $\sqrt{\frac{ab}{2a^2+bc+ca}}+\sqrt{\frac{bc}{2b^2+ca+ab}}+\sqrt{\frac{ca}{2c^2+ab+bc}}\ge\frac{81}{2}\cdot\frac{abc}{(a+b+c)^3}$

Prove that $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\le\frac{3}{\sqrt{7}}$

Seeking concise proof: $\frac18(a^2+b^2)(b^2+c^2)(c^2+a^2)\ge\frac1{27}(ab+bc+ca)^3$, where $a$, $b$, $c$ are positive numbers

If the sum of cubes of $a,b,c,d$ is $1$, then $\frac{1}{1-bcd}+\frac{1}{1-cda}+\frac{1}{1-dab}+\frac{1}{1-abc}\le \frac{16}{3}$

Prove that $\sum\limits_{\mathrm{cyc}}{\frac{1}{(x+2y)^2}} \geq\frac{1}{xy+yz+zx}$ for $x, y, z > 0$

Hard inequality $ (xy+yz+zx)\left(\frac{1}{(x+y)^2}+\frac{1}{(y+z)^2}+\frac{1}{(z+x)^2}\right)\ge\frac{9}{4} $

How prove this $x^3+y^3+z^3+3\ge 2(x^2+y^2+z^2)$

How prove this inequality$4(a^2+b^2+c^2)+9a^2b^2c^2\ge 21$

prove that $a^2 b^2 (a^2 + b^2 - 2) \ge (a + b)(ab - 1)$

An elegant but difficult inequality.

Finding maximum with two constraints

Prove $(\frac{x^2}{y}+\frac{y^2}{z}+\frac{z^2}{x})^3+12\ge 13(x^3+y^3+z^3)$ for positives $xyz = 1$

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

Trending Questions

Popular # Hahtags

Popular Questions