The arithmatic mean of 2 no is 34 and geomatric mean of two no is 16 then nos will be

• Let the 2 nos. be 'a' and 'b'
  Arithmetic mean=(a+b)/2=34 i.e. a+b=68 -----------eqn.1
  Geometric mean=(ab)^(1/2)=16 i.e. ab=256
  a-b=[(a+b)^2}-4ab]^(1/2)
  or, a-b= [(68^2)-(4*256)]^(1/2)=60-------------------eqn.2
  Solving eqn.1 &2 we get--
  a=64 & b=4
  Answer: two nos are 64 & 4
• 10 years agoHelpfull: Yes(42) No(1)
• A.M of a and b=>(a+b)/2=34=> a+b=68---(1)
  G.M of a and b=>sqrt(a,b)=16=> ab=256
  (a-b)^2=(a+b)^2-4ab= (68)^2-(4*256)=>4624-1024=> 3600
  (a-b)^2=3600=> a-b=60------(2)
  Solving (1) and (2), we get
  b=4, a=64
• 10 years agoHelpfull: Yes(9) No(0)
• use the options, it will be quicker :P
• 10 years agoHelpfull: Yes(7) No(0)
• let nos are a,b
  so A.M = (a+b)/2= 34
  -----> a+b=68
  G.M. sqrrot of ab=16
  -----> ab=16*16
  soving them a=64, b=4
• 10 years agoHelpfull: Yes(4) No(1)
• a+b /2 =34
  (ab)^1/2 =16
  taking different case of a and b we gt a=4 b=64
• 10 years agoHelpfull: Yes(1) No(0)
• i think it can be 2 solutions
  a=4 and b=64
  a=64 and b=4
  
  if i take 1 case
  a+b/2 that is 4+64/2=34
  sqrt(4*64)=16
  
  if i take 2 case
  a+b/2 ie 64+4/2=34
  sqrt(64*4)=16
• 9 years agoHelpfull: Yes(1) No(1)
• From experience the equation will be
  a^2-(34x2)a+16^2=0
  a^-68a+256=0
  Solving..
  a = 4 or 64
  That's the two numbers.
• 10 years agoHelpfull: Yes(0) No(0)
• (X+Y)/2 = 34
  SQRT(XY)= 16
  (X-Y)^2= (X+Y)^2 - 4XY
  ANS = 4 AND 64
• 10 years agoHelpfull: Yes(0) No(0)
• arithmatic mean (a+b)/2=34
  geometric mean sqrt(ab)=16
  so
  a+b=68
  ab=16*16 that is 16*4*4 = 64*4( its sum is 68)
  so the numbers are 64 and 4
• 10 years agoHelpfull: Yes(0) No(0)
• x+y/2=34;xy^1/2=16
  x,y=4,64 or 64,4
• 9 years agoHelpfull: Yes(0) No(0)
• a+b=68 -->equ 1
  ab=256 -->equ 2
  b=256/a
  sub b in 1
  a+256/a=68
  a^2 + 256=68a
  a^2-68a+256=0
  a=4 or 64
  ans : a= 4, b=64 or a=64 ,b=4
• 9 years agoHelpfull: Yes(0) No(0)