geometric mean

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.