Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem K. 100. (November 2006)

K. 100. Solve the following equation on the set of real numbers: x^2+6+\frac{1}{x^2}=4x+\frac{4}{x}.

(6 pont)

Deadline expired on December 11, 2006.


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

Megoldás. Nagyon gyorsan jutunk a megoldáshoz, ha észrevesszük, hogy (x+1/x-2)2=0 alakra rendezhető az egyenlet (x\neq0). Vagyis x+1/x-2=0, amiből x2-2x+1=0, azaz (x-1)2=0. Az egyedüli megoldás:x=1.


Statistics:

180 students sent a solution.
6 points:109 students.
5 points:19 students.
4 points:12 students.
3 points:1 student.
2 points:9 students.
1 point:14 students.
0 point:16 students.

Problems in Mathematics of KöMaL, November 2006