Question

有多少个实数x,使得函数y=（x²-2x+4）/（x²-3x+3）的值为整数?

Answer 1

A=(x^2-2x+4)/(x^2-3x+3)=[(x^2-3x+3)+x+1]/(x^2-3x+3)=1+(x+1)/(x^2-3x+3)

设(x+1)/(x^2-3x+3)=K

则：Kx^2-(3K+1)x+3K-1=0

△=(3K+1)^2-4k(3K-1)>=0

则(10-√112）/6