List questions from sum-of-squares-method | MathQa

Prove that $\sqrt{x_1}+\sqrt{x_2}+\cdots+\sqrt{x_n} \geq (n-1) \left (\frac{1}{\sqrt{x_1}}+\frac{1}{\sqrt{x_2}}+\cdots+\frac{1}{\sqrt{x_n}} \right )$

Published on 13 Jan 2025 - 1:19

Prove that $a\sqrt{a^2+bc}+b\sqrt{b^2+ac}+c\sqrt{c^2+ab}\geq\sqrt{2(a^2+b^2+c^2)(ab+ac+bc)}$

Published on 13 Jan 2025 - 1:14

inequality with three variables and condition

Published on 13 Jan 2025 - 0:56

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 13 Jan 2025 - 1:15

Prove that $m_a(bc-a^2)+m_b(ac-b^2)+m_c(ab-c^2) \geq 0.$

Published on 13 Jan 2025 - 0:59

Prove that $\frac{a}{b+2c+3d}+\frac{b}{c+2d+3a}+\frac{c}{d+2a+3b}+\frac{d}{a+2b+3c} \geq \frac{2}{3}.$

Published on 13 Jan 2025 - 1:13

Question about an inequality which seems right but not easy to prove

Published on 13 Jan 2025 - 1:08

prove that $(ab+bc+ca)\bigg(\frac{a}{b(a^2+2b^2)}+\frac{b}{c(b^2+2c^2)}+\frac{c}{a(c^2+2a^2)}\bigg) \ge 3$

Published on 13 Jan 2025 - 1:14

Show that $(a + b)^4 + (a + c)^4 + (a + d)^4 + (b + c)^4 + (b + d)^4 + (c + d)^4 \le 6$ for $a^2 + b^2 + c^2 + d^2 = 1$.

Published on 13 Jan 2025 - 1:10

Nesbitt by Nesbitt

Published on 12 Jan 2025 - 17:17