Question

Prove that: $a^{12}+b^{12}+c^{12} \geq \frac{2049}{8}\cdot a^4b^4c^4 $

score 146 · Answer 1 · 2021-08-26 09:55:34

146

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Prove that: $a^{12}+b^{12}+c^{12} \geq \frac{2049}{8}\cdot a^4b^4c^4 $

Published on 26 Aug 2021 - 9:55

score 405 · Answer 2 · 2026-03-26 21:10:14

405

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Let $a,b,c$ be non-negative real numbers .Prove that : $ a^2+b^2+c^2 +\sqrt{2} abc + 2\sqrt{2} +3 \geq (2+\sqrt {2} )(a+b+c) $

Published on 26 Mar 2026 - 21:10

score 345 · Answer 3 · 2026-03-25 18:49:36

345

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If $x + y + z = 1$, what is $\min(xyz)$ where $x$, $y$ and $z$ are positive numbers?

Published on 25 Mar 2026 - 18:49

score 105 · Answer 4 · 2026-03-25 19:17:44

105

Views

Problem in normalization inequalities

Published on 25 Mar 2026 - 19:17

score 468 · Answer 5 · 2021-09-09 22:14:02

468

Views

Finding $x^8+y^8+z^8$, given $x+y+z=0$, $\;xy +xz+yz=-1$, $\;xyz=-1$

Published on 09 Sep 2021 - 22:14

score 116 · Answer 6 · 2021-09-10 17:18:58

116

Views

Proving an identiy on elementary symmetric polynomials

Published on 10 Sep 2021 - 17:18

score 55 · Answer 7 · 2026-03-27 14:58:25

55

Views

Why do we consider the lower bound in this Inequality?

Published on 27 Mar 2026 - 14:58

score 855 · Answer 8 · 2021-09-20 18:43:01

855

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I want to show that the polynomial below has integer coefficients.

Published on 20 Sep 2021 - 18:43

score 2.4k · Answer 9 · 2021-09-22 02:54:58

2.4k

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Find value of $x^{5} + y^{5} + z^{5}$ given the values of $x + y + z$, $x^{2} + y^{2} + z^{2}$ and $x^{3} + y^{3} + z^{3}$

Published on 22 Sep 2021 - 2:54

score 141 · Answer 10 · 2026-03-27 00:10:45

141

Views

Evaluating elementary symmetric polynomial at $n^{th}$ powers

Published on 27 Mar 2026 - 0:10

score 158 · Answer 11 · 2021-09-24 10:30:58

158

Views

Prove that for any real numbers x,y,z $3(xy+yz+zx)\le(x+y+z)^2\le3(x^2+y^2+z^2)$

Published on 24 Sep 2021 - 10:30

score 129 · Answer 12 · 2026-03-27 04:58:04

129

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Find the minimum value of $a^8+b^8+c^8+2(a-1)(b-1)(c-1)$

Published on 27 Mar 2026 - 4:58

score 453 · Answer 13 · 2026-03-26 21:09:24

453

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Prove that $\sqrt[3]{a} + \sqrt[3]{b} + \sqrt[3]{c} \ge ab + bc + ca$

Published on 26 Mar 2026 - 21:09

score 162 · Answer 14 · 2026-03-26 21:10:32

162

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How do I prove that $\sum_{cyc}\left(\dfrac{1}{x^2-xy+y^2}\right)+15\ge6(\sqrt{xy}+\sqrt{yz}+\sqrt{zx})$ given $x,y,z > 0$ and $x+y+z=3$?

Published on 26 Mar 2026 - 21:10

score 393 · Answer 15 · 2026-03-25 23:42:41

393

Views

$\mathbb C[y_1,\cdots, y_\ell]/I,$ where $I$ is generated by the relation $\sum_j(-1)^je_j h_{m-j}$ of symmetric polynomials, is $\ell!$-dimensional

Published on 25 Mar 2026 - 23:42

List Question

Prove that: $a^{12}+b^{12}+c^{12} \geq \frac{2049}{8}\cdot a^4b^4c^4 $

Let $a,b,c$ be non-negative real numbers .Prove that : $ a^2+b^2+c^2 +\sqrt{2} abc + 2\sqrt{2} +3 \geq (2+\sqrt {2} )(a+b+c) $

If $x + y + z = 1$, what is $\min(xyz)$ where $x$, $y$ and $z$ are positive numbers?

Problem in normalization inequalities

Finding $x^8+y^8+z^8$, given $x+y+z=0$, $\;xy +xz+yz=-1$, $\;xyz=-1$

Proving an identiy on elementary symmetric polynomials

Why do we consider the lower bound in this Inequality?

I want to show that the polynomial below has integer coefficients.

Find value of $x^{5} + y^{5} + z^{5}$ given the values of $x + y + z$, $x^{2} + y^{2} + z^{2}$ and $x^{3} + y^{3} + z^{3}$

Evaluating elementary symmetric polynomial at $n^{th}$ powers

Prove that for any real numbers x,y,z $3(xy+yz+zx)\le(x+y+z)^2\le3(x^2+y^2+z^2)$

Find the minimum value of $a^8+b^8+c^8+2(a-1)(b-1)(c-1)$

Prove that $\sqrt[3]{a} + \sqrt[3]{b} + \sqrt[3]{c} \ge ab + bc + ca$

How do I prove that $\sum_{cyc}\left(\dfrac{1}{x^2-xy+y^2}\right)+15\ge6(\sqrt{xy}+\sqrt{yz}+\sqrt{zx})$ given $x,y,z > 0$ and $x+y+z=3$?

$\mathbb C[y_1,\cdots, y_\ell]/I,$ where $I$ is generated by the relation $\sum_j(-1)^je_j h_{m-j}$ of symmetric polynomials, is $\ell!$-dimensional

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