Two forces are such that the sum of their magnitudes is 18N, the resultant is $\sqrt{228}$  when they are at $120°$ . Then the magnitude of the forces are

${\text{P}}^2+{\text{Q}}^2+2\text{PQ}=\text{324}\text{N}\to \left(1\right)$

$228={\text{P}}^2+{\text{Q}}^2+2\text{PQ}\left(\frac{-1}{2}\right)\left[\cos 120°=\cos \left(90+30\right)=-\sin 30°=\frac{-1}{2}\right]$

$228={\text{P}}^2+{\text{Q}}^2-\text{PQ}\to \left(2\right)$

$\text{PQ}=\frac{96}{3}=32$

$\text{PQ}=32$

$\text{P}+\text{Q}=18$

${\left(\text{P}-\text{Q}\right)}^2={\left(\text{P}+\text{Q}\right)}^2-4\text{PQ}$

$=324-4\times 32$

$=324-128$

${\left(\text{P}-\text{Q}\right)}^2=196$

$\text{P}-\text{Q}=\sqrt{196}$

$\text{P}-\text{Q}=14$

$\text{P}+\text{Q}=18$

$\underset{\_}{\text{P}-\text{Q}=14}$

$2\text{P}=4$

$\text{P}=2$

$2+\text{Q}=18$

$\text{Q}=16\text{N}$