Progressions

If three positive real numbers x, y and z satisfy y - x = z - y  and xyz = 4, then what is the minimum possible value of y?

  1. 2(1/4)
  2. 2(2/3)
  3. 2(1/3)
  4. 2(3/4)

Answer

y - x = z - y

2y = x + z

Therefore, x, y, z are in Arithmetic Progression

AM ≥ GM

(x+y+z)/3 ≥ (xyz)1/3

y ≥ 2(2/3)

The correct option is B.