Question

If for two numbers mean is 25 and hm is 9 find gm

Answer 1

let the numbers be a and b then

arthimatic mean= a+b/2

a+b/2=15 , a+b=30 , a=30-b -----------(1)

geometric mean: sqr(a.b)

sqr(a.b)=9--------------(2)

from equation 2 by replacing a by 30-b

sqr{b(30-b)}=9

by squaring both side of the equation

30b-b2=81

B2-30b+81=0

B2-3b-27b+81=0

B(b-3)-27(b-3)_=0

(b-3)(b-27)=0

B=3 ,b=27

If b=3 , then a=30-b =30-3=27

,bu if

B=27, then a=30-b=30-27=3

Therefore , the numbers are 3 and 27