The equation 166 × 56 = 8590 is valid in some base b ≥ 10 (that is 1, 6, 5, 8, 9, 0 are digits in base b in the above equation). Find the sum of all possible values of b ≥ 10 satisfying the equation.
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Please briefly explain why you feel this question should be reported.
Please briefly explain why you feel this answer should be reported.
Please briefly explain why you feel this user should be reported.
The equation 166 × 56 = 8590 is valid in some base b ≥ 10 (that is 1, 6, 5, 8, 9, 0 are digits in base b in the above equation). Find the sum of all possible values of b ≥ 10 satisfying the equation.
The equation 166 × 56 = 8590 is valid in some base b ≥ 10 (that is 1, 6, 5, 8, 9, 0 are digits in base b in the above equation). Find the sum of all possible values of b ≥ 10 satisfying the equation.
(166)a × (56)a = (8590)a
=> [a3 + 6a2 + 6] [5a + 6] = 8a3 + 9a2 + 5a
=> 3a3 – 31a2 – 57a – 36 = 0
=> (a – 12) (3a2 + 5a + 3) = 0
a = 12, only possible value of a.