Question 6273: Find two numbers with a geometric mean of sqrt 24 given that one number is two more than the other.
Answer by xcentaur(357)   (Show Source):
You can put this solution on YOUR website! let the numbers be a and b.
then geometric mean=(a+b)/2
given second number is two greater that first,b=a+2
therefore geometric mean=(a+a+2)/2=(2a+2)/2=[2(a+1)]/2=(a+1)
From the question,it is required geometric mean be equal to sqrt24.
Then we get,
a+1=sqrt(24)
(a+1)=sqrt(2*2*2*3)
(a+1)=2sqrt(6)
a=2sqrt(6)-1
then value of b=a+2
=2sqrt(6)-1+2
=2sqrt(6)+1
cross check:
geometric mean of [2sqrt(6)-1] and [2sqrt(6)+1] is=
={[2sqrt(6)-1]+[2sqrt(6)+1]}/2
={2[2sqrt(6)]}/2
=2sqrt(6)
which is equal to sqrt(24)
Hence these numbers are correct
[2sqrt(6)-1]
[2sqrt(6)+1]
Hope this helps,
good luck.
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