Find the base K of the number system, if (524)8 = (664)K ?

• base K = 7.
  
  5*8^2 + 2*8^1 + 4*8^0 = 6*K^2 + 6*K^1 + 4*K^0
  320 + 16 + 4 = 6(K^2) + 6K + 4
  340 = 6(K^2) + 6K + 4
  6(K^2) + 6K + 4 - 340 = 0
  6(K^2) + 6K - 336 = 0
  dividing by 6;
  (K^2) + K - 56 = 0
  
  solving this quadratic equation we get, K=7 and K=-8
  thus K=7 is the answer.
• 14 years agoHelpfull: Yes(5) No(0)
• they are two values 7,-8
  as where k is a base ,we consider positigve value of k i.e k=7
  correct ans :7
  
• 10 years agoHelpfull: Yes(0) No(0)