Permutations and Combinations

Question

The A.M. of two numbers is 3 times their G.M. Show that the numbers are in the ratio

Let a and b be two numbers.
A.M =   G.M. =
According to the given condition
Applying componendo and dividendo, we get

Again applying componendo and dividendo, we get

Squaring both sides, we get

∴    Numbers are in ratio