Question

The sum of two numbers is 15 and than their geometric mean is 20%lower than their arithemetic mean find the numbers

Answer 1

let a and b be two numbers
then a+b =15. Equation 1

and also GM = 20% lower
that is GM is 80% of AM
8/20(a+b) = root ab
2/5(a+b) = square root(a*b)
a+b is 15
therefore
2*15/5 = square root(a*b)
36 = ab
put b=36/a in Equation 1
a + 36/a = 15
a^2 - 15*a +36 = 0
a = (15+9)/2 = 12
hence b =3
or
a = (15-9)/2 = 3
b =12

two numbers are 12 and 3