Question

The Harmonic mean between two numbers is 9/5
and their geometric mean is
3. Find the numbers.
.​

Answer 1

Answer:

Nos are 9& 1

Step-by-step explanation:

given GM=3 and HM=9/5

let the nos are x and y

• formula of  GM of two nos a and b  is  

⇒GM^2=a*b

3^2=X*Y

X*Y=9 ,⇒ 1/Y=X/9

• formula of  HM of nos(n) a and b, ,,

⇒ n/H.M=1/a+1/b

so, 1/X+1/Y=2*5/9 .    

1/X+X/9=10/9 ,,,,, SUBSTITUTING 1/Y=X/9

9/X+X=10

9+X^2=10X

X^-10X+9=0

X^-X-9X+9=0

X(X-1)-9(X-1)=0

(X-9)*(X-1)=0

⇒X=9 OR 1,

NOW,SINCE,,,,X*Y=9,

CONSIDER,X=9 THEN 9*Y=9

⇒Y=1