Current location - Training Enrollment Network - Mathematics courses - Mathematics is a compulsory course in senior high school. Theorem of mean inequality. Please help me explain why the arithmetic mean of a number is greater than or equal to its geometric mean. observe
Mathematics is a compulsory course in senior high school. Theorem of mean inequality. Please help me explain why the arithmetic mean of a number is greater than or equal to its geometric mean. observe
a+b-2√(ab)

=(√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.