Let a and b be natural numbers. If a2 + ab + a = 14 and b2 + ab + b = 28, then (2a + b) equals
Explanation:
Given a and b are natural numbers.
a2 + ab + a = 14 ⇒ a(a + b + 1) = 14 = 1 × 14 or 2 × 7
Case 1: a = 1 and a + b + 1 = 14 ⇒ b = 12 a = 1 and b = 12 does not satisfy b2 + ba + b = 28
Case 2: a = 2 and a + b + 1 = 7 ⇒ b = 4 a = 2 and b = 4 satisfies b2 + ba + b = 28
∴ 2a + b = 4 + 4 = 8
Hence, option (c).
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