y=x²+2x+5-2✔(x²+2x+3)=x²+2x+3-2✔(x²+2x+3)+2= ｛✔(x²+2x+3)-1｝²+2∵ x²+2x+3=(x+1)²+2≥2∴✔(x²+2x+3)≥✔2∴｛✔｛x²+2x+3-1｝²≥(✔2-1)²∴ y=｛✔(x²+2x+3)-1｝²+2≥5-2✔2∴值域：【5-2✔2，+∞)
