Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem C. 1161. (March 2013)

C. 1161. The real numbers a, b, c in the equation satisfy a+b+c=0, abc=-48, and bc+ac+ab=-28. Solve the equation.

(5 pont)

Deadline expired on April 10, 2013.

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

Megoldás. Az eredeti egyenlet így írható:

$\displaystyle \frac{x+a}{a}+\frac{x+b}{b}+\frac{x+c}{c}=10,$

$\displaystyle \frac xa+\frac xb+\frac xc=7.$

Vagyis: $\displaystyle x=7:\left(\frac1a+\frac1b+\frac1c\right)=7\cdot\frac{abc}{bc+ac+ab}=7\cdot\frac{-48}{-28}=12$.

### Statistics:

 228 students sent a solution. 5 points: 191 students. 4 points: 12 students. 3 points: 6 students. 2 points: 11 students. 1 point: 3 students. 0 point: 3 students. Unfair, not evaluated: 2 solutions.

Problems in Mathematics of KöMaL, March 2013