List questions from tangent-line-method | MathQa

$ x+y+z = 3, \; \sum\limits_{cyc} \frac{x}{2x^2+x+1} \leq \frac{3}{4} $

Published on 13 Apr 2025 - 9:38

Prove that $\frac{bc}{a^2+bc}+\frac{ca}{b^2+ca}+\frac{ab}{c^2+ab}\le{\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b}}$

Published on 07 Apr 2025 - 4:27

Chebyshev's sum inequality

Published on 05 Apr 2025 - 10:37

Prove that $\sum \frac{x}{x^2+7}\le \frac{3}{8}$

Published on 19 Apr 2025 - 4:22

inequality under condition $x+y+z=3$

Published on 18 Apr 2025 - 17:27

Inequality with 5 cyclic variables

Published on 18 Apr 2025 - 19:36

Proving $\sum_{cyc} \sqrt{a^2+ab+b^2}\geq\sqrt 3$ when $a+b+c=3$

Published on 13 Apr 2025 - 10:53

Prove that the minimum values of $x^2+y^2+z^2$ is $27$ with given condition $\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}=1$.

Published on 07 Apr 2025 - 4:13

Find all positive real solutions of the system

Published on 18 Apr 2025 - 14:59

Inequality $\sum_{cyc}a^3\frac{(16a^2-10ab+12b^2)}{(13a^2+5b^2)^2}\geq \frac{a+b+c}{18}$

Published on 19 Apr 2025 - 12:12