Problem C. 826.

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C. 826. Solve the following equation:

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

(5 points)

Deadline expired.

Sorry, the solution is published in Hungarian only.

Alakítsuk az egyenletet (x $\neq$ 1):

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

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

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 on problem C. 826.

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

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