The arithmetic mean is the average of two numbers.
(x + y) ÷ 2 = 25
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
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.