[tex]x*y=3x+3y-xy-6=-xy+3x+3y-9+3=\\
=-x(y-3)+3(y-3)+3=-(y-3)(x-3)+3=\\
=-(x-3)(y-3)+3\\
x*y*z=-(x*y-3)(z-3)+3=\\
=-(-(x-3)(y-3)+3-3)(z-3)+3=\\
=(x-3)(y-3)(z-3)+3\\
\text{Punand in cele doua relatii obtinute } y=x, \text{ apoi }z=y=x:\\
x*x=-(x-3)^2+3,\\
x*x*x=(x-3)^3+3
\\
\text{Se poate demonstra prin inductie ca:}
\\ x^{(2n)}=-(x-3)^{2n}+3,
\\ x^{(2n+1)}=(x-3)^{2n+1}+3, \forall n\in N^*
\\ \text{Cum $2014$ estete par,} \\ x^{(2014)}= -(x-3)^{2014}+3=x\Rightarrow -(x-3)^{2014}=x-3\\
\Rightarrow x-3=0 \text{ sau }x-3=-1 \Rightarrow x=3 \text{ sau } x=2[/tex],
\\
