Question

If the A.M. and G.M. between two numbers are respectively 17 and 8, find the numbers.

Answer 1

let a and b be the two numbers

a+b/2=A.M.=17
=>a+b=34.......................................(1)
√ab=GM=8
=>ab=64
(a+b)^2=(a-b)^2+4ab
(34)^2 - 4(64)=(a-b)^2
(a-b)=√900
a-b=+30 or - 30.............(2)
if a-b=+30 then from (1)
a=32,b=2
if a-b= - 30 then from (1)
a=2, b=32


therefore the numbers are 2 and 32


I hope this will help