# Math Help - help with Lucas numbers

1. ## help with Lucas numbers

Given $L_{1}=1,L_{2}=3,L_{n+2}=L_{n}+L_{n+1}$, how can I prove that $L_{3}=\alpha^3-\alpha^{-3}$ where $\alpha=\frac{1+\sqrt{5}}{2}$??

2. If you are supposed to find $L_3$, then just check if the equality hold or not.
If you are supposed to find the formulla of $L_n$, the characteristic equation $x^2-x-1=0$(can you find the roots)will help you.