I3.1 If $\alpha+\beta=11, \alpha \beta=24$ and $\alpha>\beta$, find $\alpha$.
I3.2 If $\tan \theta=\frac{-\alpha}{15}, 90^{\circ}<\theta<180^{\circ}$ and $\sin \theta=\frac{b}{34}$, find $b$.
13.3 If $A$ is the area of a square inscribed in a circle of diameter $b$, find $A$.

I3.4 If $x^{2}+22 x+A \equiv(x+k)^{2}+d$, where $k, d$ are constants, find $d$.
$\alpha$ and $\beta$ are the roots of the equation $x^{2}-11 x+24=0$
$$
\begin{array}{l}
(x-3)(x-8)=0 \\
\because \alpha>\beta \therefore \alpha=8
\end{array}
$$

In the figure, $P=(8,-15)$
$r^{2}=8^{2}+(-15)^{2}$ (Pythagoras' theorem)
$$
\begin{array}{l}
r=17 \\
\sin \theta=\frac{8}{17}=\frac{16}{34} \\
b=16
\end{array}
$$

Let the square be $B C D E$.
$$
\begin{array}{l}
B C=16 \cos 45^{\circ}=8 \sqrt{2} \\
A=(8 \sqrt{2})^{2}=128 \\
x^{2}+22 x+128 \equiv(x+11)^{2}+7 \\
d=7
\end{array}
$$