Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem C. 871. (November 2006)

C. 871. Prove that if the expression

\frac{x^2}{(x-y)(x-z)} +\frac{y^2}{(y-x)(y-z)} +\frac{z^2}{(z-x)(z-y)}

is well defined, then its value is independent of the values of the variables x, y and z.

(5 pont)

Deadline expired on December 15, 2006.

Sorry, the solution is available only in Hungarian. Google translation

Megoldás. Közös nevezőre hozva, majd a zárójeleket felbontva:



428 students sent a solution.
5 points:401 students.
4 points:2 students.
3 points:1 student.
1 point:6 students.
0 point:14 students.
Unfair, not evaluated:4 solutionss.

Problems in Mathematics of KöMaL, November 2006