Question

If the ratio of AM to GM of two positive numbers a and b is 5:3, then a:b is equal to

Answer 1

Answer:

a : b = 9 : 1

Step-by-step explanation:

Formula used:

Arithmetic mean of two positive numbers x and y is

$\frac{x+y}{2}$

Geometic mean of two positive numbers x and y is

$\sqrt{xy}$

Assume that a>b

Given:

A.M : G.M = 5:3

A.M= 5k and G.M= 3k

$\frac{a+b}{2}=5k$ and $\sqrt{ab}=3k$

$a+b=10k$ and $ab=9k^2$

By trial and error method we get

a=9k and b=k

Now,

a : b = 9k : k

a : b = 9 : 1