# SOLUTION: Find two numbers with a geometric mean of sqrt 24 given that one number is two more than the other.

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 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.