Problem: The number of roots satisfying the equation 5βxβ=x5βxβ is:
Answer Choices:
A. unlimited
B. 3
C. 2
D. 1
E. 0
Solution:
Replace 5βxβ=x5βxβ by
5βx=x2(5βx)
The soiution set for this equation is {5,1,β1} but the solution set for the original equation is {5,1}.
5βxβ=x5βxβ
If 5βxξ =0, divide by 5βxβ and obtain x=1
If 5βx=0, then x=5