List questions from buffalo-way | MathQa

Prove that $\left | \frac{a-b}{a+b}+\frac{b-c}{b+c}+\frac{c-a}{c+a} \right | < \frac{1}{8}.$

Published on 13 Jan 2025 - 5:19

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

Published on 13 Jan 2025 - 1:05

Inequality in 4 variables Vasc's EV

Published on 13 Jan 2025 - 6:00

Proving an interesting inequality with square roots

Published on 13 Jan 2025 - 7:37

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 13 Jan 2025 - 7:41

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

Published on 13 Jan 2025 - 7:40

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 13 Jan 2025 - 1:18

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 13 Jan 2025 - 7:53

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 13 Jan 2025 - 7:53

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

Published on 13 Jan 2025 - 7:51