1.用直接开平方法解下列方程：
(1)$3x^2 -27=0$；
(2)$(2x+1)^2=9$；
(3)$3(x+1)^2 -108=0$。

(1)解:$3x^2=27$,$x^2=9$,$x_1=3$,$x_2=-3$.
(2)解:$2x+1=\pm 3$. $\therefore 2x+1=3$ 或 $2x+1=-3$. $\therefore x_1=1$,$x_2=-2$.
(3)解:$3(x+1)^2=108$,$(x+1)^2=36$. $\therefore x+1=\pm 6$. $\therefore x_1=5$,$x_2=-7$.

2. 用配方法解下列方程：
(1)$x^2 - 2x - 99 = 0$；
(2)$2x^2 - 4x - 3 = 0$。

(1)解:$x^2-2x=99$,$x^2-2x+1=99+1$,即$(x-1)^2=100$. $\therefore x-1=\pm10$. $\therefore x_1=11$,$x_2=-9$.
(2)解:$x^2-2x=\frac{3}{2}$,$(x-1)^2=\frac{5}{2}$,$x-1=\pm\frac{\sqrt{10}}{2}$,$\therefore x_1=1+\frac{\sqrt{10}}{2}$,$x_2=1-\frac{\sqrt{10}}{2}$.

3. 用公式法解下列方程：
(1)$2x^2 + 2x - 1 = 0$；
(2)$3x^2 - 2x - 8 = 0$。

(1)解:$\because a=2$,$b=2$,$c=-1$,$\therefore \Delta=b^2-4ac=2^2-4×2×(-1)=12＞0$. $\therefore x=\frac{-2\pm\sqrt{12}}{2×2}=\frac{-2\pm2\sqrt{3}}{4}=\frac{-1\pm\sqrt{3}}{2}$. $\therefore x_1=\frac{-1+\sqrt{3}}{2}$,$x_2=\frac{-1-\sqrt{3}}{2}$.
(2)解:$\because a=3$,$b=-2$,$c=-8$,$\therefore \Delta=b^2-4ac=(-2)^2-4×3×(-8)=100＞0$. $\therefore x=\frac{2\pm\sqrt{100}}{2×3}=\frac{2\pm10}{6}$. $\therefore x_1=2$,$x_2=-\frac{4}{3}$.