Question

HELLP PLZ SOMEONE HELLP MEEEE

Answer 1

The answer is "
`x_k= -(9)/(16) (-2)^k + (9)/(16) 2^k +(3)/(8) k* 2^k\\\\`"

Explanation:

`\to F(Z)=(3z(z-1))/(z^3-2z^2-4z+8)\\\\\to (F(Z))/(z)=(3z(z-1))/(z(z^3-2z^2-4z+8))\\\\\to (F(Z))/(z)=(3(z-1))/((z^3-2z^2-4z+8))\\\\\to (F(Z))/(z)=-(9)/(16) (1)/(z+2) + (9)/(16) (1)/(z-2) +(3)/(4) (1)/((z-2)^2)\\\\\to F(Z)=-(9)/(16) (z)/(z+2) + (9)/(16) (z)/(z-2) +(3)/(4) (z)/((z-2)^2)\\\\\to x_k= -(9)/(16) (-2)^k + (9)/(16) 2^k +(3)/(8) k* 2^k\\\\`