Find the ratio a/b.

Replies

• 

  sfdgfdh

  rengaraj

  Sir / madam,
  My question is
  
  The arithmetic mean of two positive numbers a and b is equal to twice their geometric mean. Find the ratio a/b.
  
  Advance Thanks,
  R.Rengaraj

  The arithmetic mean of two positive numbers a and b is equal to twice their geometric mean. Find the ratio a/b.
  _______________
  comparatifmutuelle.orgcomparatifmutuelle.orgcomparatifmutuelle.org
• 

  Hussanal Faroke

  (a+b)/2 = 2*root(ab)
  (a+b)=4*root(ab)
  sqr(a+b)=16ab..................................(1)
  sqr(a+b)-sqr(a-b)=2ab-(-2ab)
  =4ab
  ie, sqr(a-b)+4ab= sqr(a+b)
  =16ab [:-eq(1)]
  sqr(a-b) = 12ab ....................(2)
  
  (2)/(1) sqr(a+b)/sqr(a-b) = 16ab/12ab
  =4/3
  find square root of both side
  (a+b)/(a-b) = +,- 2/root(3)
  if 2/root(3),
  2a-2b = root(3)a +root(3)b
  (2-root(3))a =(2+root(3))b
  a/b=(2+root(3))/(2-root(3))
  
  find the result for negtive root urself, i think above proof is correct. if any mistake u find pls inform me! my id: #-Link-Snipped-#
• 

  rengaraj

  Dear Faroke,
  You gave a brilliant solution.
  Thanks,
  R.Rengaraj