12 Considere una sucesión de enteros positivos $x_n$ tal que: \[(\text{A})\ x_{2n+1}=4x_n+2n+2 \] \[(\text{B})\ x_{3n+\color[rgb]{0.9529,0.0980,0.0118}2}=3x_{n+1}+6x_n \] para todo $n\ge 0$ . Demuestre que \[(\text{C})\ x_{3n-1}=x_{n+2}-2x_{n+1}+10x_n \] para todo $n\ge 0$ .