Question

The arithmetic mean of two numbers is 9 and their geometric mean is 3√5. Find these numbers

Answer 1

(a+b)/2 = 9

so
a+b = 18

sqrt ( a b) = 3 sqrt 5
so
a b = 9*5 = 45

well so b = 45/a
and
a + 45/a = 18
or
a^2 - 18 a + 45 = 0
( a-15)(a-3) = 0
a = 15 or 3
so one of them is 3 and one of them is 15