Answer
a) $d_o=7cm$
b) $d_o=3cm$
Work Step by Step
$f=5cm$
$m=2.5$
a) $d_o=\frac{1}{\frac{1}{5cm}-\frac{1}{d_i}}$
$\frac{d_i}{d_o}=2.5$
$d_o=\frac{1}{\frac{1}{5cm}-\frac{1}{2.5d_o}}$
$d_o=\frac{12.5d_o}{2.5d_o-5cm}$
$2.5d_o-5cm-12.5cm=0$
$d_o=7cm$
b) $d_o=\frac{1}{\frac{1}{5cm}-\frac{1}{d_i}}$
$\frac{d_i}{d_o}=-2.5$
$d_o=\frac{1}{\frac{1}{5cm}-\frac{1}{-2.5d_o}}$
$d_o=\frac{12.5d_o}{2.5d_o+5cm}$
$2.5d_o+5cm=12.5cm$
$d_o=3cm$