Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation

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Problem C. 815. (September 2005)

C. 815. The product of the real numbers a and b is 1, and

$\frac{a+b+2}{4}=\frac{1}{a+1}+\frac{1}{b+1}.$

Find the values of a and b.

(5 pont)

Deadline expired on October 17, 2005.

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

Megoldás. Szorozzuk az egyenlet mindkét oldalát 4(a+1)(b+1)-gyel (a $\neq$ -1, b $\neq$ -1). Ha elvégezzük a műveleteket és minden esetben ab helyére 1-et írunk, akkor az a²+b² egyenletet kapjuk. Megoldjuk az

a²+b²=2

ab=1

egyenletrendszert. Megoldás: a=1, b=1.

Statistics:

781 students sent a solution.

5 points: 366 students.

4 points: 303 students.

3 points: 39 students.

2 points: 11 students.

1 point: 25 students.

0 point: 15 students.

Unfair, not evaluated: 22 solutionss.

Problems in Mathematics of KöMaL, September 2005

781 students sent a solution.
5 points:	366 students.
4 points:	303 students.
3 points:	39 students.
2 points:	11 students.
1 point:	25 students.
0 point:	15 students.
Unfair, not evaluated:	22 solutionss.