# The ratio of two positive real numbers is #p+sqrt(p^2-q^2):p-sqrt(p^2-q^2)#then find their ratio of AM and GM?

##### 2 Answers

#### Explanation:

Let the nos. be

By what is given,

Now, the **AM**

**GM**

Clearly,

#### Explanation:

I am going to use the same notation as in this answer . In fact there is no real necessity of this solution (as the problem has already been solved quite nicely) - except that it illustrates the use of a technique I love very much!

According to the problem

Using componendo and dividendo (this is the favorite technique I alluded to above) we get

- which is the required AM : GM ratio.