Question

If the


a.M. Of two numbers is 34 and the g.M. Of the same two numbers is 16, find the greater number. Note:


a.M = arithmetic mean & g.M = geometric mean

Answer 1

Answer:

let the two numbers in consideration be

a and b.

give;

=> A.M.=34

=> (a+b)/2=34

=> a+b=34×2

=> a+b=68 ------(1)

also;

=> G.M.= 16

=> √(ab)=16

=> ab=(16)^2 ----------(2)

now , we know that,

=> (a-b)^2 = (a+b)^2 – 4ab

=> (a-b)^2 = (68)^2 – 4(16)^2

=> (a-b)^2 = 3600

=> a-b=60 -------(3)

now , adding eq--(1) and (3)

we get,

=> 2a=128

=> a=64.

thus, using eq--(1)

=> b=68-a

=> b=68-64

=> b=4

thus the greater number is 64.

I hope it would help you

thank you