The arithmetic mean and geometric mean of two numbers are 25 and 20 respectively. Find the smaller number.
+23245 If the two numbers are 'a' and 'b'
-- the arithmetic means is (a + b)/2 = 25
-- the geometric mean is sqrt(a·b) = 20
sqrt(a·b) = 20 --> a·b = 400 ---> b = 400/a
substituting this into the other equation: (a + b)/2 = 25
---> [ a + (400/a) ] / 2 = 25
---> [ a + (400/a) ] = 50
---> a2 + 400 = 50a
---> a2 - 50a + 400 = 0
---> (a - 40)(a - 10) = 0
So, the answers are 40 and 10 ---> 10 is the smaller answer.
