Mathematical and Physical Journal
for High Schools
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Problem C. 826. (November 2005)

C. 826. Solve the following equation:


\frac{3x^3}{x^3-1}- \frac{x}{x-1}=2.

(5 pont)

Deadline expired on December 15, 2005.


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

Alakítsuk az egyenletet (x\neq1):

{3x^3\over(x-1)(x^2+x+1)}-{x\over x-1}=2,

{3x^3-x(x^2+x+1)\over(x-1)(x^2+x+1)}=2,

3x3-(x3+x2+x)=2(x3-1),

x2+x-2=0.

x1=-2, x2=1.

A kikötés miatt csak az x=-2 a megoldása az egyenletnek.


Statistics:

539 students sent a solution.
5 points:419 students.
4 points:57 students.
3 points:31 students.
2 points:6 students.
1 point:2 students.
0 point:6 students.
Unfair, not evaluated:18 solutions.

Problems in Mathematics of KöMaL, November 2005