Problem C. 852.

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

(5 points)

Deadline expired.

Sorry, the solution is published in Hungarian only.

Megoldás: Értelmezési tartomány: minden valós x.

$x^2+3-3\sqrt{x^2+3}-4\leq0,$

$\left(\sqrt{x^2+3}-4\right)\left(\sqrt{x^2+3}+1\right)\leq0.$

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

Statistics on problem C. 852.

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

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