When do the geometric and the arithmetic means of a and b coincide? only in the case when a (use a sign < ,> etc.) b

The geometric mean is
  √(ab)

The arithmetic mean is
  (a+b)/2

These are equal when
  (a+b)/2 = √ab
  a + b = 2√ab
  (a +b)² = 4ab . . . . square both sides
  a² +2ab +b² = 4ab . . . . expand the square of the binomial
  a² -2ab +b² = 0 . . . . . . subtract the right side
  (a -b)² = 0 . . . . . . . . . . . write as a square
  a -b = 0 . . . . . . . . . . . . . take the square root
  a = b . . . . . . . . . . . . . . . add b

The arithmetic and geometric means of a and b are equal when ...
  a = b