Let $a$ and $b$ be the two roots of $x^2 - 3x -1=0$. Try to solve the following problems without computing $a$ and $b$: 1) Find a quadratic equation whose roots are $a^2$ and $b^2$ 2) Find the value of $\frac{1}{a+1}+\frac{1}{b+1}$ 3) Find the recursion relationship of $x_n=a^n + b^n$ Find as many different solutions as possible.