Let b be a positive integer and a = b2 – b. If b ≥ 4, then a2 – 2a is divisible by
Explanation:
a2 – 2a = a(a – 2)
Substituting a = b2 – b, we get,
a2 – 2a = (b2 – b)[(b2 – b) – 2]
= b(b – 1)(b2 – b – 2)
= b(b – 1)(b – 2)( b + 1)
= (b – 2)(b – 1)b(b + 1)
This is a product of 4 consecutive positive integers which will definitely have a multiple of 2, 3 and 4.
∴ This must be divisible by 2 × 3 × 4 = 24
Hence, option (c).
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