=(√a) square +(√b) square -2 √ a √ b
=(√a-√b) squared
≥0
∴ ? a+b≥2√(ab)
∴ ? (a+b)/2≥√(ab)
Pay attention to the significance of geometric average is:
The area of a square is equal to the area of a rectangle whose length and width are a and b respectively.
The side length of this square is the geometric average of a and B.