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If a + 1/b =  b + 1/c = c + 1/a, where a ≠ b ≠ c ≠ 0, then the value of a2b2c2 is

If a + 1/b =  b + 1/c = c + 1/a, where a ≠ b ≠ c ≠ 0, then the value of a2b2c2 is Correct Answer 1

Calculation:

Given,

⇒ a + 1/b = b + 1/c = c + 1/a

⇒ a - b = 1/c - 1/b = (b - c)/bc 

⇒ bc = (b - c)/(a - b)

Similarly,

⇒ ab = (a - b)/(c - a)

⇒ ca = (c - a)/(b - c)

⇒ a2b2c2 = (ab)(bc)(ca) = (b - c)/(a - b) × (a - b)/(c - a) × (c - a)/(b - c) = 1

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