Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation

Already signed up?
New to KöMaL?

Problem C. 848. (March 2006)

C. 848. Find the largest and smallest values of the expression

$\sqrt{x-2}+\sqrt{3- x}.$

(5 pont)

Deadline expired on April 18, 2006.

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

Megoldás: Az $f(x)=\sqrt{x-2}+\sqrt{3-x}$ függvény pozitív értékeket vesz csak fel, ezért pontosan ott van a maximuma és a minimuma, ahol a négyzetének. $f^2(x)=2\sqrt{(x-2)(3-x)}+1$ . Ennek (és f(x)-nek is) legkisebb értéke 1, amit x=2 és x=3 esetén vesznek fel. A legnagyobb értéket pedig x=2,5 esetén veszik fel, ekkor $f(x)=\sqrt2$ .

Statistics:

290 students sent a solution.

5 points: 171 students.

4 points: 16 students.

3 points: 62 students.

2 points: 22 students.

1 point: 9 students.

0 point: 7 students.

Unfair, not evaluated: 3 solutionss.

Problems in Mathematics of KöMaL, March 2006

290 students sent a solution.
5 points:	171 students.
4 points:	16 students.
3 points:	62 students.
2 points:	22 students.
1 point:	9 students.
0 point:	7 students.
Unfair, not evaluated:	3 solutionss.