A two stage-discrete time system's formula ise

$\displaystyle x(k+1)=-x(k)+u(k)$ and $\displaystyle x(0)=10$

With dynamic prgramming find $\displaystyle u(0)$ and $\displaystyle u(1)$

which minimize

$\displaystyle J=x^2(2) + \sum_{k=0}^1 \{ x^2(k) + u^2(k)\}$

There are no restrictions on $\displaystyle u(k)$

Thank your for your help