A={yIy2-(a2+a+1）y+a（a2+1）〉0}
= { y| (y -a)(y-(a^2+1)) > 0 }
if a> a^2+1
=> a^2-a+1 < 0
=> (a-1/2)^2 + 3/4 < 0 (rejected )
ie a< a^2+1
=> A ={ y | y > a^2+1 or y < a }
B={yIy=1/2x2-x+5/2,0≤x≤3 }
let
f(x) = (1/2)x^2 -x +5/2
f'(x) = x-1 = 0
x = 1
f''(x) = 1 > 0 ( min)
min f(x) = f(1) = 2
f(0)= 5/2
f(3) = 9/2 - 3 + 5/2 = 4
=> B = { x| 2≤x≤4 }
A∩B＝ø
=> { y | y > a^2+1 or y < a } ∩ { x| 2≤x≤4 } ＝ø
=> a^2+1 > 4 and a < 2
=> (a > √3 or a< -√3 ) and a< 2
=> √3 < a < 2
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