When numbers are written in base b we have 12x25=333. the value of b is?
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Given : numbers are written in base b we have 12 x 25 = 333
To Find : Value of b
Solution:
12 x 25 = 333
12 = 1* b¹ + 2b⁰ = b + 2
25 = 2*b¹ + 5b⁰ = 2b + 5
333 = 3b² + 3b¹ + 3b⁰ = 3b² + 3b + 3
(b + 2)(2b + 5) = 3b² + 3b + 3
=> 2b² + 9b + 10 = 3b² + 3b + 3
=> b² - 6b - 7 = 0
=> b² - 7b + b - 7 = 0
=> b(b - 7) + 1(b - 7) = 0
=> (b + 1)(b - 7) = 0
=> b = - 1 , b = 7
base can not be -ve
Hence b = 7
Value of b is 7
(12)₇ x (25)₇ = (333)₇
9 x 19 = 171
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