Question 42
The sequence $(f_i)_{i=0}^{\infty}$ is defined by $f_0 = f_1 = 1$ and $f_{i+2} = f_{i+1} + f_i$ ($i \ge 0$).
Find all real solutions of the equation
$$
x^{2010} = f_{2009}x + f_{2008}.
$$
Find all real solutions of the equation
$$
x^{2010} = f_{2009}x + f_{2008}.
$$