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akshatseanjamip2hjto
@akshatseanjamip2hjto
September 2021
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If the A.M. and G.M. between two numbers are respectively 17 and 8, find the numbers.
Answers & Comments
beast14
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
22 votes
Thanks 32
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Answers & Comments
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