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

(6 points)

This problem is for grade 9 students only.

Deadline expired on 11 December 2006.


Google Translation (Sorry, the solution is published in Hungarian only.)

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 on problem K. 100.
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

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