8. Let $f(x)=x^{2}+12 x+30$. Find the largest real root of the equation $f(f(f(x)))=0$.
(1 mark)設 $f(x)=x^{2}+12 x+30$ 。求方程 $f(f(f(x)))=0$ 的最大實根。
(1 分)
8. $-6+\sqrt[8]{6}$
8. By completing square we have $f(x)=(x+6)^{2}-6$ and so
$$
f(f(x))=\left(\left((x+6)^{2}-6\right)+6\right)^{2}-6=(x+6)^{4}-6 .
$$

Similarly, $f(f(f(x)))=(x+6)^{8}-6$. The equation thus becomes $(x+6)^{8}=6$, with solutions $x=-6 \pm \sqrt[8]{6}$. Hence the answer is $-6+\sqrt[8]{6}$.