The arithmetic mean between two numbers is 75 and their geometric mean is 21. Find the numbers.
+23252 If the two numbers are a and b:
arithmetic mean = (a + b) / 2 ---> (a +b) / 2 = 75 ---> a + b = 150
geometric mean = sqrt(a·b) ---> sqrt(a·b) = 21 ---> ab = 441 ---> b = 441 / a
Combining: a + 441 / a = 150 ---> a2 + 441 = 150a ---> a2 - 150a + 441 = 0
Using the Quadratic Formula: a = [ 150 +/- sqrt( 20736) ] / 2 ---> 147 or 3
a is one of the two possibilities; b is the other.
+23252 If the two numbers are a and b:
arithmetic mean = (a + b) / 2 ---> (a +b) / 2 = 75 ---> a + b = 150
geometric mean = sqrt(a·b) ---> sqrt(a·b) = 21 ---> ab = 441 ---> b = 441 / a
Combining: a + 441 / a = 150 ---> a2 + 441 = 150a ---> a2 - 150a + 441 = 0
Using the Quadratic Formula: a = [ 150 +/- sqrt( 20736) ] / 2 ---> 147 or 3
a is one of the two possibilities; b is the other.
