Let $l,a_1$ positive real numbers and define the sequence term $a_{n+1}=\frac{1}{2} \left( a_n + \frac{l^2}{a_n} \right)$. Prove $(a_n)$ is decreasing

Question

Let $l,a_1$ positive real numbers and define the sequence term $a_{n+1}=\frac{1}{2} \left( a_n + \frac{l^2}{a_n} \right)$. Prove that the sequence $(a_n)$ is strictly decreasing for $n \geq 2$

I tried to use induction. I could do the base case. Then, with the hypothesis that $\dfrac{a_k}{a_{k-1}}<1$ for any $k \in \mathbb{N}$ I tried the induction step and got stuck on $\dfrac{a_{k+1}}{a_k}=\dfrac{(a_k^2+l^2)a_{k-1}}{a_k(a_{k-1}^2+l^2)}$. I hope someone could provide me a hand.