I1.3 Given that $p$ and $q$ are real numbers with $p q=b$ and $p^{2} q+q^{2} p+p+q=70$. If $c=p^{2}+q^{2}$, find the value of $c$.
$$
p q=9 \ldots(1) \text {, and } p q(p+q)+(p+q)=70 \Rightarrow(p q+1)(p+q)=70 \ldots
$$

Sub. (1) into (2): $10(p+q)=70 \Rightarrow p+q=7 \ldots$ (3)
$$
c=p^{2}+q^{2}=(p+q)^{2}-2 p q=7^{2}-2 \times 9=31
$$

Remark: The original question is Given that $p$ and $q$ are integers with $p q=b$ and $p^{2} q+q^{2} p+p+q=70$. However, $p q=9, p+q=7$, which give no integral solution.