The A.M. between two positive numbers is 34 and their GM. is 16. Find the numbers.
Let a and b be two numbers
A.M. = 34 ...(i)
G.M. = 16 ...(ii)
From (i), b = 68 - a
Using in (ii), we get
a(68 - a) = 256
a(a - 64) - 4 (a - 64) = 0
(a - 64) (a - 4) = 0
a = 4, 64
When a = 4, b = 68 - 4 = 64
and a = 64, b = 68 - 64 = 4