a为何值时,不等式(a^2-3a+2)*x^2+(a+1)*x+2>0的解是一切实数?

题目

a为何值时,不等式(a^2-3a+2)*x^2+(a+1)*x+2>0的解是一切实数?

答案

(a^2-3a+2)*x^2+(a+1)*x+2>0
(a+1)*(a+2)*(x^2+x/(a+2)+1/4(a+2)^2)+2-(a+1)/4(a+2)>0
(a+1)(a+2)*(x+1/2a+4)^2+(8a+16-a-1)/(4a+8)>0
(a+1)(a+2)>=0,(8a+16-a-1)/(4a+8)>=0,
a=-1,a>=-2,a=-1,a