Question

The arithmetic mean and geometric mean
between two numbers are 75 and 21
respectively, then the numbers are​

Answer 1

Answer:

Let the two numbers be a and b.

So the arithmetic mean between a and b = (a+b)/2

=> (a+b)/2 = 17

=> a+b = 34

=> b = 34-a (i)

The geometric mean between a and b = square root( ab)

=> square root( ab) = 8

Squaring both the sides,

=> ab = 64

=> a ( 34-a )= 64

=>34a-a2 = 64

=> a2 -34a+64= 0

=> a2 - 32a – 2a+ 64 = 0

=> a(a-32)- 2(a-32) = 0

=> (a-32) (a-2) =0

Therefore, when a=2 then

b = 34-a

=34-2

=32

Or

When a=32 then

b = 34-32

= 2

So the two numbers are (2,32)