Problem: The number of roots satisfying the equation 5−x​=x5−x​ is:
Answer Choices:
A. unlimited
B. 3
C. 2
D. 1
E. 0
Solution:
Replace 5−x​=x5−x​ by
5−x=x2(5−x)
The soiution set for this equation is {5,1,−1} but the solution set for the original equation is {5,1}.
5−x​=x5−x​
If 5−xî€ =0, divide by 5−x​ and obtain x=1
If 5−x=0, then x=5