35,80,135 are three numbers in the bases a,b & c resp.35,80,& 135 correspond to 120 in base 10 system. a,b,c are in which progression?

• is anything is not missing there PRASAD REDDY KUNDURI ???
• 11 years agoHelpfull: Yes(14) No(0)
• given that base of 35 is a, base of 80 is b and base of 135 is c and they all are equal to 120 in decimal number system, that is base 10.
  (35)a=(80)b=(135)c=(120)10
  then 120 base 10 is actually 120 itself
  equate 35 base a to 120
  i.e. (35)a=120
  then by conversion the above can be written as
  3a+5=120 -> 3a=120-5 -> 3a=115 -> a=115/3 -> a=38.33333
  again equate 80 base b to 120
  i.e. (80)b=120
  then by conversion the above can be written as
  8b+0=120 -> 8b=120 -> b=15
  once again equate 135 base c to 120
  i.e. (135)c=120
  then by conversion the above can be written as
  c^2+3c+5=120 -> c^2+3c-115=0
  calculate roots for c^2+3c-115=0 take the negative root
  that is "c" could be equal to -12.32
  Now compare the values of a,b,c
  a=38.3, b=15, c=-12.3
  difference between them is equal
  so, the roots are in Arithmetic progression
• 11 years agoHelpfull: Yes(12) No(2)