Let a and b be natural numbers. If a² + ab + a = 14 and b² + ab + b = 28, then (2a + b) equals
Question:
Let a and b be natural numbers. If a² + ab + a = 14 and b² + ab + b = 28, then (2a + b) equals
Let a and b be natural numbers. If a² + ab + a = 14 and b² + ab + b = 28, then (2a + b) equals
Options
Answer: 8
Explanation:
a(a + b + 1) = 14 so a ∈ {1,2,7,14}. a = 1 ⇒ 1(1 + b + 1) = 14 ⇒ b = 12 (fails second equation). a = 2 ⇒ 2(2 + b + 1) = 14 ⇒ b = 4. Check: b² + ab + b = 16 + 8 + 4 = 28 ✓ a = 7 or 14 give nonpositive b. Thus a = 2, b = 4 ⇒ 2a + b = 2·2 + 4 = 8.
Explanation:
a(a + b + 1) = 14 so a ∈ {1,2,7,14}. a = 1 ⇒ 1(1 + b + 1) = 14 ⇒ b = 12 (fails second equation). a = 2 ⇒ 2(2 + b + 1) = 14 ⇒ b = 4. Check: b² + ab + b = 16 + 8 + 4 = 28 ✓ a = 7 or 14 give nonpositive b. Thus a = 2, b = 4 ⇒ 2a + b = 2·2 + 4 = 8.
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