Question

If the arithmetic mean is 34 and geometric mean is 16 then these tw no are

Answer 1

if the arithmetic mean is 34, the sum of
the two number is 68
call the two number x, 68-x
if the geometric mean is 16, the product
is 256
x(68-x) =256
68x -x^2 =256
x^2 -68x +256=0
(x-64)(x-4)=0
numbers are 4 and 64, so a. 4

Answer 2

let two numbers be 'a,b'
arithmetic mean = a+ b/2
a+b/2=34
a+b=34×2
a+b=68
a=68-b

geometric mean=
$\sqrt{ab}$
=16
ab =16²
b(68-b)=256
68b-b²=256
b²-68b+256=0
b²-64b-4b+256=0
b(b-64)-4(b-64)=0
(b-4)(b-64)=0
b=4 (or) 64
so those two numbers are 4 and 64
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