G. 1 The sum of two numbers is 50 , and their product is 25 .
If the sum of their reciprocals is $a$, find $a$.

SG. 2 If the lines $a x+2 y+1=0$ and $3 x+b y+5=0$ are perpendicular, find $b$.
SG. 3 The area of an equilateral triangle is $100 \sqrt{3} \mathrm{~cm}^{2}$. If its perimeter is $p \mathrm{~cm}$, find $p$.
SG. 4 If $x^{3}-2 x^{2}+p x+q$ is divisible by $x+2$, find $q$.
Let the 2 numbers be $x, y$.
$$
\begin{array}{l}
x+y=50, x y=25 \\
\Rightarrow a=\frac{1}{x}+\frac{1}{y} \\
=\frac{x+y}{x y} \\
=\frac{50}{25}=2 \\
2 x+2 y+1=0 \text { is } \perp \text { to } 3 x+b y+5=0 \\
\Rightarrow \text { product of slopes }=-1 \\
-\frac{2}{2} \times \frac{-3}{b}=-1 \\
\Rightarrow b=-3 \\
\end{array}
$$

Let the length of one side be $x \mathrm{~cm}$.
$$
\begin{array}{l}
\frac{1}{2} x^{2} \sin 60^{\circ}=100 \sqrt{3} \\
\Rightarrow x=20 \\
\Rightarrow p=60 \\
\text { Let } f(x)=x^{3}-2 x^{2}+60 x+q \\
f(-2)=-8-8-120+q=0 \\
q=136
\end{array}
$$