x=a²-2b+1,y=b²-2c+2,z=c²-2b+3,求x+y+z的取值范围
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![x=a²-2b+1,y=b²-2c+2,z=c²-2b+3,求x+y+z的取值范围](/uploads/image/z/14613321-57-1.jpg?t=x%3Da%26%23178%3B-2b%2B1%2Cy%3Db%26%23178%3B-2c%2B2%2Cz%3Dc%26%23178%3B-2b%2B3%2C%E6%B1%82x%2By%2Bz%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4)
x=a²-2b+1,y=b²-2c+2,z=c²-2b+3,求x+y+z的取值范围
x=a²-2b+1,y=b²-2c+2,z=c²-2b+3,求x+y+z的取值范围
x=a²-2b+1,y=b²-2c+2,z=c²-2b+3,求x+y+z的取值范围
x + y + z = a² - 2b + 1 + b² -2c + 2 + c² - 2b + 3
= a² + b² - 4b + 4 - 4 + c² - 2c + 1 - 1 + 1 + 2 + 3
= a² + (b-2)² + (c-1)² + 1
显然, x + y + z >= 1, 当 a = 0, b = 2, c = 1 时, 取等号
取值范围
大于或等于1