Question 54
If $$a + \frac{1}{b} = 1$$ and $$b + \frac{1}{c} = 1$$, then what is the value of abc?
Solution
$$a + \frac{1}{b} = 1$$
ab + 1 = b
$$b + \frac{1}{c} = 1$$
bc + 1 = c
Putting value of b, we get:
(ab + 1)c + 1 = c ==> abc + c + 1 = c
This gives value of abc = -1.
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