If A and G are the AM and GM respectively between the two numbers then the numbers are
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Let the numbers be a,b.
Given , A = (a+b)/2 and G = √(ab) ....(1)
(a+b)² = 4A²
(a²+b²) = 4A²–2G²
(a–b)² = 4(A²–G²)
(a–b) = 2√(A²-G²)....(2)
from , equations (1) and (2), we get
a = A+√(A²–G²)
b = A–√(A²–G²).
Given , A = (a+b)/2 and G = √(ab) ....(1)
(a+b)² = 4A²
(a²+b²) = 4A²–2G²
(a–b)² = 4(A²–G²)
(a–b) = 2√(A²-G²)....(2)
from , equations (1) and (2), we get
a = A+√(A²–G²)
b = A–√(A²–G²).
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