  Let $p_1\equiv p_2\equiv5 \pmod8$ be prime numbers such that
$\left(\frac{p_1}{p_2}\right)=-1$. Let $\mathbb{L}=Q(\sqrt2, \sqrt{p_1p_2})$
Our goal is to resolve the equation
$X^2-\varepsilon_2\varepsilon_{p_1p_2}\varepsilon_{2p_1p_2}=0$ in $\mathbb{L}$,
where $\varepsilon_j$ are fundamental units of real quadratic subfields of
$Q(\sqrt2, \sqrt{p_1p_2})$.
