Mathematical and Physical Journal
for High Schools
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Problem C. 881. (January 2007)

C. 881. Solve the equation \left(\frac{x}{2}\right)^{2} =\left(\frac{x+1}{3}\right)^{3}.

(5 pont)

Deadline expired on February 15, 2007.


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

Megoldás: x=2 megoldás. Beszorzás és átalakítás után:

0=4x3-15x2+12x+4=(x-2)(4x2-7x-2)=(x-2)(x-2)(x+1/4).

(A harmadfokú függvényt ábrázolva sejthető, hogy az (x-2)2-nel is oszható.)

Tehát a megoldások x1=2 és x2=-1/4.


Statistics:

372 students sent a solution.
5 points:262 students.
4 points:31 students.
3 points:14 students.
2 points:18 students.
1 point:28 students.
0 point:6 students.
Unfair, not evaluated:13 solutions.

Problems in Mathematics of KöMaL, January 2007