1.5 The Fibonacci numbers $1,1,2,3,5,...$ are defined by the recursion formula $x_{n+1} = x_n + x_{n-1}$, with $x_1 = x_2 = 1$. Prove that $(x_n, x_{n+1}) = 1$ and that $x_{n} = \frac{a^n -b^n}{a-b}$ where $a,\text{and }b $ are roots of quadratic equation $1 +x-x^2=0$.
I just need help here $x_{n} = \frac{a^n -b^n}{a-b}$