Let a, b, c be positive integers such that b a is an integer. If a, b, c are in geometric progression and the arithmetic mean of a, b, c is b + 2, then the value of a 2 + a - 14 a + 1   is ________

Question

Let a, b, c be positive integers such that b a is an integer. If a, b, c are in geometric progression and the arithmetic mean of a, b, c is b + 2, then the value of a 2 + a - 14 a + 1 &#160; is ________

Aicharya · Accepted Answer

b c = c b = i n t e g e r b 2 = a c ⇒ c = b 2 a a + b + c 3 = b + 2 a + b + c = 3 b + 6 ⇒ a - 2 b + c = 6 a - 2 b + b 2 a = 6 ⇒ 1 - 2 b a + b 2 a 2 = 6 a b a - 1 2 = 6 a ⇒ a = 6 only

Let a, b, c be positive integers such that b a is an integer. If a, b, c are in geometric progression and…

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