Question

The
a.M of two numbers is 6.5 and their g.M is 6 find the numbers

Answer 1

Answer:

9  and 4

Step-by-step explanation:

Let the two numbers be a and b .

Now Arithmetic Mean of a and b  = (a+b) / 2   = 6.5

or,  (a+b)  = 6.5 x 2  = 13

So, a +  b  =13 ................................   (1)

Now, Geometric Mean of a and b is $\sqrt{ab}$

⇒   $\sqrt{ab}$  = 6

Squaring both sides, we get

ab = 36

Substitute a  =  13 - b   from (1)

⇒   (13 - b) b = 36

or, $- b^{2} + 13b  = 36$

⇒ $b^{2}  - 13b  + 36 = 0$

Solving for b , we get either b = 4 or b = 9

if b = 4, a = 13- 4 = 9

if b = 9. a =  13-9  = 4

Both answers are correct according to the given condition.