Question

find two number whose arithmetic Mean is 34 and GP is 16

Answer 1

Let the numbers be x, y  

Then arithmatic mean = (x+y)/2 =34  

→x+y =68  

Also geometric mean =√(xy)=16  

oy xy=16²=256  

Hence  

x(68−x)=256  

or x²−68x+256=0  

(x−64)(x−4)=0  

Hence x=64 or x=4  

and y=4 or 64  

Larger number is 64

Answer 2

Let the numbers be x, y
Then arithmatic mean = (x+y)/2 =34
→x+y =68
Also geometric mean =√(xy)=16
oy xy=16²=256
Hence
x(68−x)=256
or x²−68x+256=0
(x−64)(x−4)=0
Hence x=64 or x=4
and y=4 or 64
Larger number is 64