ivan
Reputation
1,048
Top tag
Next privilege 2,000 Rep.
3 16
Impact
~24k people reached

 8 How to prove this inequality $\sqrt{\frac{ab+bc+cd+da+ac+bd}{6}}\geq \sqrt[3]{{\frac{abc+bcd+cda+dab}{4}}}$ 6 Inequality. $\sqrt{\frac{11a}{5a+6b}}+\sqrt{\frac{11b}{5b+6c}}+\sqrt{\frac{11c}{5c+6a}} \leq 3$ 5 How can one prove that $\pi^4 + \pi^5 < e^6$? 4 The definition of “number” 3 Combinatorially equivalent polyhedra?

### Reputation (1,048)

 +10 How to prove $\frac{\pi^2}{6}\le \int_0^{\infty} \sin(x^{\log x}) \ \mathrm dx$? +10 Inequality.$\sqrt{\frac{2a}{b+c}}+\sqrt{\frac{2b}{c+a}}+\sqrt{\frac{2c}{a+b}} \leq 3$ -2 Prove the Inequality: $\sum\frac{x^3}{2x^2+y^2}\ge\frac{x+y+z}{3}$ +10 How to prove this inequality $\sqrt{\frac{ab+bc+cd+da+ac+bd}{6}}\geq \sqrt[3]{{\frac{abc+bcd+cda+dab}{4}}}$

### Questions (5)

 8 A difficult symmetric inequality 5 Power means inequality 4 Is this AM/GM refinement correct or not? 3 Ellipse and circles 0 On a AM/GM refinement

### Tags (36)

 45 inequality × 31 3 logarithms × 2 6 reference-request × 2 3 polyhedra 5 real-analysis × 3 3 terminology 4 calculus × 3 3 combinatorial-geometry 4 definition 2 analysis × 2

### Accounts (7)

 Mathematics 1,048 rep 316 MathOverflow 305 rep 39 Stack Overflow 265 rep 28 Super User 101 rep 1 English Language & Usage 101 rep