4x+1-(x²+5)
=-x²+4x-4
=-(x²-4x+4)
=-(x-2)²
x=2时,(x-2)²=0 -(x-2)²=0 4x+1=x²+5
x≠2时,(x-2)²>0-(x-2)²<04x+1综上,得4x+1≤x²+5 (当且仅当x=2时取等号)