Question

使得分式括号x减一括号的三次方分之2x的平方减4x加二的值为整数的x的整数值有

Answer 1

(2x^2-4x+2)/(x-1)^3=2(x-1)^2/(x-1)^3=2/(x-1)=n

x=1+2/n 为整数,n=2^m (m=1,0,-1,...)

使得分式(2x^2-4x+2)/(x-1)^3的值为整数的x的整数值有:n=2^m (m=1,0,-1,-2,...)