x²-2x+3=(x-1)²+2≥2
∴ 1/(x²-2x+3)∈(0,1/2]
∴ 4/(x²-2x+3)∈(0,2]
∴ √[4/(x²-2x+3)]∈(0,√2]
即根号下4除以（x平方-2X+3）的值域为(0,√2]