Question

若关于x的方程（x-5）\(x-6)-(x-6)\(x-5）=k\(x-5)(x-6)的解不大于13,求k的取值范围

Answer 1

x≠5,x≠6

k＝(x-5)^2-(x-6)^2＝(x-5+x-6)(x-5-x+6)＝2x-11

x=(k+11)/2

因为x≠5,x≠6,x≤13

所以,(k+11)/2≠5,(k+11)/2≠6,(k+11)/2≤13

k≠-1,k≠1,k≤15