方程(a-x²)/(a-x)²-1/a=(a-1)/[a³-ax(2a-x)]的正整数解x为_________.当解为正整数时,a应

题目

方程(a-x²)/(a-x)²-1/a=(a-1)/[a³-ax(2a-x)]的正整数解x为_________.当解为正整数时,a应

答案

[a³-ax(2a-x)]=a(a-x)²方程化为：a(a-x²)-(a-x)²=a-1即-(x-1)²a=x²-1=(x-1)(x+1)------>x=1或-(x-1)a=x+1x=1或x=(a-1)/(a+1)x=1.a=(1+x)/(1-x)