Question

Find $|\overline{a}|$ and $|\overline{b}|$ if ($\overline{a}$ +$\overline{b}$) + ($\overline{a}$ - $\overline{b}$) = 8 and $|\overline{a}|$ = 8 $|\overline{b}|$

Answer 1

Given $(\overline{a}+\overline{b})+(\overline{a}-\overline{b})=8\Rightarrow 2\overline{a}=8\Rightarrow |\overline{a}|=4$

We also know that $|\overline{a}|=8|\overline{b}|$

Therefore $|\overline{b}|=\frac{|\overline{a}|}{8}=\frac{1}{2}$

$\Rightarrow |\overline{a}|=8,|\overline{b}|=\frac{1}{2}$