List questions from muirhead-inequality

138

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for $x,y,z\ge 0$, $x+y+z=2$, prove $\frac{x}{1+y^2}+\frac{y}{1+z^2}+\frac{z}{1+x^2}\ge\frac{18}{13}$

Published on 19 Mar 2026 - 19:59

130

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Inequality with powers of 2

Published on 20 Mar 2026 - 1:17

159

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Prove this Hard inequality to CS or AM-GM?

Published on 20 Mar 2026 - 14:47

366

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Inequality involving cyclic sums (Muirhead? Schur? Something else?)

Published on 20 Mar 2026 - 1:51

124

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Inequality with $abc=1$,

Published on 20 Mar 2026 - 13:52

91

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Muirhead's inequality -- equality occur

Published on 20 Mar 2026 - 19:23

277

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Proof of Muirhead's inequality

Published on 22 Mar 2026 - 4:38

100

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An inequality with a condition

Published on 18 Mar 2026 - 0:34

163

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Prove $\sum\limits_{cyc}\frac{1}{x^{2017}+ x^{2015}+ 1} \geq 1$ with $x,\,y,\,z>0,\,xyz= 1$

Published on 22 Mar 2026 - 8:00

196

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Inequality from AMM problems section

Published on 20 Mar 2026 - 4:53

106

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If $a$, $b$ and $c$ are positive then $\sum\limits_{cyc} \frac{a^{2}}{b^{2}+c^{2}+bc}\geq 1$

Published on 20 Mar 2026 - 5:20

148

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Prove: $x^4 + y^4 + z^4 - 4(x^3 + y^3 + z^3) + 5(x^2 + y^2 + z^2) \leqslant 4 $

Published on 25 Mar 2026 - 1:18

213

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Show that $\frac {1}{3+x^2+y^2} + \frac {1}{3+y^2+z^2} +\frac{1} {3+x^2+z^2}\leq \frac {3}{5} . $

Published on 25 Mar 2026 - 4:43

257

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Proving $\sum\limits_{\text{cyc}} \frac{a}{b^2+c^2+d^2} \geq \frac{3\sqrt{3}}{2}\frac{1}{\sqrt{a^2+b^2+c^2+d^2}}$ for $a, b, c, d >0$

Published on 19 Mar 2026 - 22:28

62

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Inequality using lengths of the edges of a triangle

Published on 25 Mar 2026 - 1:17

List Question

for $x,y,z\ge 0$, $x+y+z=2$, prove $\frac{x}{1+y^2}+\frac{y}{1+z^2}+\frac{z}{1+x^2}\ge\frac{18}{13}$

Inequality with powers of 2

Prove this Hard inequality to CS or AM-GM?

Inequality involving cyclic sums (Muirhead? Schur? Something else?)

Inequality with $abc=1$,

Muirhead's inequality -- equality occur

Proof of Muirhead's inequality

An inequality with a condition

Prove $\sum\limits_{cyc}\frac{1}{x^{2017}+ x^{2015}+ 1} \geq 1$ with $x,\,y,\,z>0,\,xyz= 1$

Inequality from AMM problems section

If $a$, $b$ and $c$ are positive then $\sum\limits_{cyc} \frac{a^{2}}{b^{2}+c^{2}+bc}\geq 1$

Prove: $x^4 + y^4 + z^4 - 4(x^3 + y^3 + z^3) + 5(x^2 + y^2 + z^2) \leqslant 4 $

Show that $\frac {1}{3+x^2+y^2} + \frac {1}{3+y^2+z^2} +\frac{1} {3+x^2+z^2}\leq \frac {3}{5} . $

Proving $\sum\limits_{\text{cyc}} \frac{a}{b^2+c^2+d^2} \geq \frac{3\sqrt{3}}{2}\frac{1}{\sqrt{a^2+b^2+c^2+d^2}}$ for $a, b, c, d >0$

Inequality using lengths of the edges of a triangle

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