I2.2 If $x+y=P, x^{2}+y^{2}=Q$ and $x^{3}+y^{3}=P^{2}$, find the value of $Q$.
$\begin{array}{l}x+y=3, x^{2}+y^{2}=Q \text { and } x^{3}+y^{3}=9 \\ (x+y)^{2}=3^{2} \Rightarrow x^{2}+y^{2}+2 x y=9 \Rightarrow Q+2 x y=9 \ldots \ldots \text { (1) } \\ (x+y)\left(x^{2}+y^{2}-x y\right)=9 \Rightarrow 3(Q-x y)=9 \Rightarrow Q-x y=3 \ldots \ldots \\ (1)+2(2): 3 Q=15 \Rightarrow Q=5\end{array}$