Mathematical and Physical Journal
for High Schools
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Problem C. 852. (April 2006)

C. 852. Solve the following inequality on the set of real numbers: x^2-3\sqrt{x^2+3}\le 1.

(5 pont)

Deadline expired on May 18, 2006.

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

Megoldás: Értelmezési tartomány: minden valós x.



A második tényező minden x-re pozitív, ezért \sqrt{x^2+3}\leq4, azaz x2\leq13. Vagyis a megoldás: x\in\left[-\sqrt{13};\sqrt{13}\,\,\right].


243 students sent a solution.
5 points:114 students.
4 points:49 students.
3 points:43 students.
2 points:23 students.
1 point:7 students.
0 point:7 students.

Problems in Mathematics of KöMaL, April 2006