The geometric mean of two numbers is 3, and their arithmetic mean is 5. What is the sum of their reciprocals?

Question

The geometric mean of two numbers is 3, and their arithmetic mean is 5. What is the sum of their reciprocals?

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Answer 1

10/9

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Answer 2

given,
geometric mean=3
so,(a*b)^1/2=3
a*b=9
b=a/9.
given,
arithmetic mean=5
so,a+b/2=5
a+b=10
putting the value of b in the above expression
a+a/9=10
(9a+a)/9=10
10a=90
a=9
we know,a+b=10(from above)
9+b=10
b=1
therefore the numbers are 9 & 1
sum of their reciprocals
=1/9+1
=(1+9)9
=10/9(answer)

Answer 3

rtxy=3
xy=9
x+y/2=5
x+y=10
9/y +y=10
multiplying by y
9+y^2=10y
y^2-10y+9=0
(y-9)(y-1)=0
y=9 or 1
if y=9 x=1 and if y=1 x=9
the nos. are1,9 or 9,1 resply
the sum of the recipreocals
=1/9+1
=10/9 or 1 1/9

Answer 4

1/a + 1/b = (a+b)/(ab) = (5*2)/(3^2) = 10/9.

Answer 5

sqrt(a b) = 3
(a + b) /2 = 5

ab = 9
a+b = 10
(1/a) +(1/b) = (a+b)/(ab) = 10/9

Answer 6

let a,b be two no.s
then (a+b)/2=5
(ab)^(1/2)=3
s=1/a +1/b=(a+b)/ab=10/9=1.111...