若x=a²-2b+1,y=b²-2c+2,z=c²-2a+3,求x+y+z的取值范围
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若x=a²-2b+1,y=b²-2c+2,z=c²-2a+3,求x+y+z的取值范围
若x=a²-2b+1,y=b²-2c+2,z=c²-2a+3,求x+y+z的取值范围
若x=a²-2b+1,y=b²-2c+2,z=c²-2a+3,求x+y+z的取值范围
x+y+z=a²+b²+c²-2a-2b-2c+6
x+y+z=(a-1)²+(b-1)²+(c-1)²+3
∵(a-1)²≥0,(b-1)²≥0,(c-1)²≥0
∴x+y+z≥3
x+y+z=(a-1)²+(b-1)²+(c-1)²+3
∴x+y+z€[3,+∞)