If the arithmetic mean of two numbers is 25, and the geometric mean is seven, what are the values of the two numbers? *
The arithmetic mean is the average of two numbers.
(x + y) ÷ 2 = 25
Solve
Multiply both sides by 2
x + y = 50
To calculate the geometric mean of two numbers, multiply the numbers together and take the square root.
√xy = 7
Solve
Square both sides
xy = 49
Answer: the numbers are 1 and 49.
Check: 1 + 49 = 50
*I had the assistance of Quora contributor Elaine Dawe, BMath, Mathematics and Computer Science, University of Waterloo 1985.
The arithmetic mean is the average of two numbers.
(x + y) ÷ 2 = 25
Solve
Multiply both sides by 2
x + y = 50
To calculate the geometric mean of two numbers, multiply the numbers together and take the square root.
√xy = 7
Solve
Square both sides
xy = 49
Answer: the numbers are 1 and 49.
Check: 1 + 49 = 50
*I had the assistance of Quora contributor Elaine Dawe, BMath, Mathematics and Computer Science, University of Waterloo 1985.
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