Problem: If the distinct non-zero numbers x(y−z),y(z−x),z(x−y) form a geometric progression with common ratio r, then r satisfies the equation
Answer Choices:
A. r2+r+1=0
B. r2−r+1=0
C. r4+r2−1=0
D. (r+1)4+r=0
E. (r−1)4+r=0
Solution:
Let a=x(y−z) and observe that the identity
x(y−z)+y(z−x)+z(x−y)=0
implies
a+ar+ar21+r+r2=0=0.