I3.1 Given that $\left\{\begin{array}{r}w x y z=4 \\ w-x y z=3\end{array}\right.$ and $w>0$. If the solution of $w$ is $P$, find the value of $P$.
I3.2 Let $[y]$ represents the integral part of the decimal number $y$. For example, $[3.14]=3$.
If $\left[(\sqrt{2}+1)^{p}\right]=Q$, find the value of $Q$. (Reference: HKAL PM 1991 P1 Q11, 2005 HG5)

I3.3 Given that $x_{0} y_{0} \neq 0$ and $Q x_{0}^{2}-22 \sqrt{3} x_{0} y_{0}+11 y_{0}^{2}=0$. If $\frac{6 x_{0}^{2}+y_{0}^{2}}{6 x_{0}^{2}-y_{0}^{2}}=R$, find the value of $R$.
From (2), $x y z=w-3 \ldots \ldots . \ldots . .(3)$, sub. into (1)
$$
\begin{array}{l}
w(w-3)=4 \\
w^{2}-3 w-4=0 \\
w=4 \text { or } w=-1 \text { (rejected) } \\
P=4
\end{array}
$$

Note that $0<\sqrt{2}-1<1$ and $0<(\sqrt{2}-1)^{4}<1$
$$
\begin{array}{l}
(\sqrt{2}+1)^{4}+(\sqrt{2}-1)^{4}=2\left(\sqrt{2}^{4}+6 \sqrt{2}^{2}+1\right)=2(4+12+1)=34 \\
33<(\sqrt{2}+1)^{4}<34 \\
Q=\left[(\sqrt{2}+1)^{4}\right]=33 \\
33 x_{0}^{2}-22 \sqrt{3} x_{0} y_{0}+11 y_{0}^{2}=0 \\
3 x_{0}^{2}-2 \sqrt{3} x_{0} y_{0}+y_{0}^{2}=0 \\
\left(\sqrt{3} x_{0}-y_{0}\right)^{2}=0 \\
y_{0}=\sqrt{3} x_{0} \\
R=\frac{6 x_{0}^{2}+y_{0}^{2}}{6 x_{0}^{2}-y_{0}^{2}}=\frac{6 x_{0}^{2}+3 x_{0}^{2}}{6 x_{0}^{2}-3 x_{0}^{2}}=3
\end{array}
$$