Answer
$P_{CO_2} = 1.96 \space atm$
$P_{CO} = 2.54 \space atm$
Work Step by Step
$P_{CO_2} + P_{CO} = 4.50$
$$\frac{P_{CO}^2}{P_{CO_2}} = 1.52 \longrightarrow P_{CO_2} = \frac{P_{CO}^2}{1.52} = 0.658P_{CO}^2$$
Substituting:
$$P_{CO_2} + 0.658P_{CO_2}^2 = 4.50$$
$$P_{CO_2} = 1.96 \space atm$$
$P_{CO} = 4.50 - 1.96 = 2.54 \space atm$
