Find $| \overrightarrow a |$ and $| \overrightarrow b |$ , if $(\overrightarrow a + \overrightarrow b) ⋅ (\overrightarrow a − \overrightarrow b) = 8$ and $| \overrightarrow a |= 8 | \overrightarrow b |.$

Question

$\begin{array}{1 1}|\overrightarrow a|=\large\frac{\sqrt2}{\sqrt{63}},\:|\overrightarrow b|=\large\frac{2\sqrt 2}{\sqrt{63}} \\|\overrightarrow a|=\large\frac{16\sqrt2}{\sqrt{63}},\:|\overrightarrow b|=\large\frac{2\sqrt 2}{\sqrt{63}} \\|\overrightarrow a|=\large\frac{8\sqrt2}{\sqrt{63}},\:|\overrightarrow b|=\large\frac{\sqrt 8}{\sqrt{63}} \\ |\overrightarrow a|=\:8\sqrt{\large\frac{8}{62}},\:|\overrightarrow b|=\sqrt{\large\frac{8}{62}} \end{array}$