A sequence Problem

Algebra Level 3

The sequence $a_1,a_2,a_3,\ldots$ satisfies $a_{n+2}=\dfrac{2}{a_{n+1}}+a_n , \quad n=1,2,3,\ldots.$

with initial values $a_1=1, a_2=2$ .

Find the value of $a_{100}\times a_{101}$ .