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5. 参考例题的方法解方程.
例 解方程:$x^2 - |x| - 2 = 0$.
解:当$x \geq 0$时,原方程可化为$x^2 - x - 2 = 0$,解得$x_1 = 2$,$x_2 = -1$.
$\because x \geq 0$,$\therefore x = -1$舍去. $\therefore x = 2$是原方程的解.
当$x ＜ 0$时,原方程可化为$x^2 + x - 2 = 0$,解得$x_1 = -2$,$x_2 = 1$.
$\because x ＜ 0$,$\therefore x = 1$舍去. $\therefore x = -2$是方程的解.
综上所述,原方程的解为$x_1 = 2$,$x_2 = -2$.
解方程:$x^2 + 2|x + 2| - 4 = 0$.
例 解方程:$x^2 - |x| - 2 = 0$.
解:当$x \geq 0$时,原方程可化为$x^2 - x - 2 = 0$,解得$x_1 = 2$,$x_2 = -1$.
$\because x \geq 0$,$\therefore x = -1$舍去. $\therefore x = 2$是原方程的解.
当$x ＜ 0$时,原方程可化为$x^2 + x - 2 = 0$,解得$x_1 = -2$,$x_2 = 1$.
$\because x ＜ 0$,$\therefore x = 1$舍去. $\therefore x = -2$是方程的解.
综上所述,原方程的解为$x_1 = 2$,$x_2 = -2$.
解方程:$x^2 + 2|x + 2| - 4 = 0$.
答案：
$x_{1}=0$,$x_{2}=-2$
6. 如图,在$□ ABCD$中,$AE \perp BC于点E$,$AE = EB = EC = a$,且$a是一元二次方程2x^2 - 4x = 5(2 - x)$的根.求$□ ABCD$的周长.
答案：
$4\sqrt{2}+8$
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