The harmonic mean H of two numbers is 4 and the arithmetic mean A and geometric mean G satisfy the
equation 2A + G^2 = 27. The two numbers are
(a) 6, 3 (b) 9, 5 (c) 12, 7 (d) 3, 1

• HM= 2ab/a+b, GM= root ab ,AM=a+b/2
  so.
  2ab/a+b=4--------------- (1)
  ab=2(a+b) &
  a+b= ab/2
  &2A=a+b
  &G^2= ab
  put the value in equation which is given in question.--------
  a+b+ab= 27------------------(2)
  ab/2+ab= 27
  3ab=54
  ab=18
  or
  a+b+2(a+b)=27 ---> a+b+2a+2b=27----> 3a+3b=27---> so. a+b= 9
  so we can match the options for both value 9 &18 so ab= 18 thn 6*3=18 and a+b=9 so.. 6+3=9
• 9 years agoHelpfull: Yes(0) No(0)