I2.1 If $1000 a=85^{2}-15^{2}$, find $a$.
I2.2 The point $(a, b)$ lies on the line $5 x+2 y=41$. Find $b$.
$\mathbf{I 2 . 3} x+b$ is a factor of $x^{2}+6 x+c$. Find $c$.
I2.4 If $d$ is the distance between the points $(c, 1)$ and $(5,4)$, find $d$.
$$
\begin{array}{l}
1000 a=(85+15)(85-15)=100 \times 70 \\
\Rightarrow a=7 \\
5(7)+2 b=41 \\
\Rightarrow b=3
\end{array}
$$

Put $x=-3$ into $x^{2}+6 x+c=0$
$$
(-3)^{2}+6(-3)+c=0
$$
$$
\begin{array}{l}
\Rightarrow c=9 \\
d^{2}=(9-5)^{2}+(1-4)^{2}=25 \\
\Rightarrow d=5
\end{array}
$$