Solve the ecuation:

where [x] is the whole part of the number x and {x} is the fractional part of the number x.

Scrii x = [ x ] + { x };

Folosesti proprietatea fundamentala a proportiilor;

Apoi, exprimi [ x ] in functie de { x }, si obtii ca:

[ x ] = (2012 - { x } ^2 - 2013{ x }) / (2012 + { x });

Fie { x } = t ∈ [ 0, 1);

Obtii ca [ x ] = - t - 1 + 4024 / (t + 2012);

Stim ca [ x ] ∈ Z;

Atunci t = 0 sau t = 2012;

Convine numai t = 0 = > x = [ x ];

Ecuatia originala va avea solutia 1.

Bafta!