The arithmetic mean of 2 numbers is 34 and their geometric mean is 16. One of the numbers will be

• A.M=x+y2=34
  x+y=68
  G.M=(x.y)^1/2=16
  x.y=256
  x^2-68x+256=0
  x=4 or 64
• 13 years agoHelpfull: Yes(43) No(13)
• sum of two numbers = 2*34=68
  product of two numbers = 16*16=256
  difference of two numbers =
  sqrt[(sum*sum)-4(product)]=sqrt[68*68-4*256]=sqrt[3600] = 60
  therefore, one no. is = "64" ,........other no. is = "4"
• 13 years agoHelpfull: Yes(18) No(18)
• Let the numbers be x, y
  Then arithmatic mean = (x+y)/2 =34
  →x+y =68
  Also geometric mean =√(xy)=16
  oy xy=16²=256
  Hence
  x(68−x)=256
  or x²−68x+256=0
  (x−64)(x−4)=0
  Hence x=64 or x=4
  and y=4 or 64
  Larger number is 64
  3 years ago
• 11 years agoHelpfull: Yes(18) No(2)
• please any one tel me where have to learn this type of question any websites or books..please suggest me
• 9 years agoHelpfull: Yes(10) No(3)
• AM = x+y/2 = 34 => x+y = 68--------(1)
  and GM = √xy =16 => xy = 256 => x = 256/y --------(2)
  substitute (2) in (1) we get roots 4, 64
  
  so, 64 gives the proper meaning
• 10 years agoHelpfull: Yes(3) No(0)
• The numbers are 4 and 64.
• 10 years agoHelpfull: Yes(1) No(0)
• (a+b)/2=34
  ab=16*16=256
  256/a+a=68
  256+a^2=68a
  on solving we get
  4 o
  r 64
  
• 8 years agoHelpfull: Yes(0) No(0)
• answer is 4 or 64.
  solution is:-
  x+y=68---------arithmetic mean
  x.y=256----------geometric mean
  64 and 4 are satisfying both equations.
• 7 years agoHelpfull: Yes(0) No(0)