Thursday, April 1, 2010

Book: "Rèn luyện kĩ năng sử dụng bất đẳng thức Cauchy - Schwarz thông qua các bài toán" (by V. Q. B. Can) will appear soon

I am writing a new inequality book named "Rèn luyện kĩ năng sử dụng bất đẳng thức Cauchy - Schwarz thông qua các bài toán." In English, it means "Improving your skills of using the Cauchy - Schwarz Inequality through problems." In the book, I presented all techniques I know about the Cauchy - Schwarz Inequality. I hope that the readers can improve their skills of using the Cauchy - Schwarz Inequality after reading this book. The book is written in Vietnamese and it will appear soon. Here is the cover (it was designed by me):

Saturday, March 20, 2010

Inequality 152 [V. Q. B. Can]

Let $a,b,c,d$ be positive real numbers. Prove that
$\frac{a^{2}-bd}{b+2c+d}+\frac{b^{2}-ca}{c+2d+a}+\frac{c^{2}-db}{d+2a+b}+\frac{d^{2}-ac}{a+2b+c}\geq 0.$

Friday, March 19, 2010

Inequality 151 [T. Q. Anh]

Let $a,b,c$ be nonnegative real numbers, no two of which are zero. Prove that
$\sum \frac{b^3+c^3}{a^2+bc}\ge 2\sum \frac{a^2}{b+c}.$