1.
4a^2-4a(a+2)＞0,
a(a-a-2)＞0,
a＜0;
y=x^2-(2a+1)x+2a-5為開口向上的拋物線
所以在x=2處,y＜0
y=2^2-(2a+1)2+2a-5
=-2a-3＜0
a＞-3/2
所以-3/2＜a＜0.
2.
x1+x2=2a/(a+2)
x1*x2=a/(a+2)
|x1|+|x2|=2√2
(|x1|+|x2|)^2=x1^2+x2^2+2|x1x2|
=x1^2+x2^2-2a/(a+2)
=x1^2+x2^2-2a/(a+2)
=(2ax1-a)/(a+2)+(2ax2-a)/(a+2)-2a/(a+2)
=(2ax1+2ax2)/(a+2)-4a/(a+2)
=2a(x1+x2)/(a+2)-4a/(a+2)
=4a^2/(a+2)^2-4a/(a+2)
=8
a^2/(a+2)^2-a/(a+2)-2=0
[a/(a+2)-2][a/(a+2)+1]=0
a/(a+2)=2或a/(a+2)=-1
a=2a+4或a+a+2=0
a=-4或a=-1
由于-3/2＜a＜0
所以a=-1.