Mathematical and Physical Journal
for High Schools
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Problem A. 414. (December 2006)

A. 414. Prove


(xy+yz+zx)
\left(\frac 1{{(x+y)}^2}+\frac1{{(y+z)}^2}+\frac1{{(z+x)}^2}\right)
\ge\frac94

for all positive reals x, y, z.

(Iranian competition problem)

(5 pont)

Deadline expired on January 15, 2007.


Statistics:

14 students sent a solution.
5 points:Blázsik Zoltán, Dobribán Edgár, Hujter Bálint, Kisfaludi-Bak Sándor, Kónya 495 Gábor, Korándi Dániel, Lovász László Miklós, Nagy 224 Csaba, Nagy 235 János, Nagy 314 Dániel, Tomon István.
3 points:1 student.
1 point:1 student.
0 point:1 student.

Problems in Mathematics of KöMaL, December 2006