If (142)_b + (112)_(b−2) = (75)_8, find the base b.
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Correct answer: D. 5
Explanation
(75)₈ = 61. (142)_b = b² + 4b + 2 and (112)_(b−2) = (b − 2)² + (b − 2) + 2. Their sum 2b² + b + 6 = 61 gives b = 5.
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