If abc - 1- then find the value of 1-1-a-b-1-1-1-b-c-1-1-1-c-a-1 -

Given expression : 1/1+a+b^ 1+1/1+b+c^ 1+1/1+c+a^ 1 =1/1+a+b^ 1+b^ 1/b^ 1+1+b^ 1c^ 1+a/a+ac+1 =1/1+a+b^ 1+b^ 1/1+b^ 1+a+a/a+b^ 1+1 =1+b^ 1+a/ ...

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Zeroes of a Polynomial

If abc = 1,...

Question

If $a b c = 1$ , then find the value of $(\frac{1}{1 + a + b^{- 1}} + \frac{1}{1 + b + c^{- 1}} + \frac{1}{1 + c + a^{- 1}})$ .

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Solution

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a b c = 1

\frac{1}{1 + a + b^{- 1}} + \frac{1}{1 + b + c^{- 1}} + \frac{1}{1 + c + a^{- 1}}

\frac{1}{1 + a + b^{- 1}} + \frac{1}{1 + b + c^{- 1}} + \frac{1}{1 + c + a^{- 1}}

\frac{1}{1 + a + b^{- 1}} + \frac{1}{1 + b + c^{- 1}} + \frac{1}{1 + c + a^{- 1}}

\frac{1}{1 + a + b^{- 1}} + \frac{1}{1 + b + c^{- 1}} + \frac{1}{1 + c + a^{- 1}}

a + b + c = 1

a^{2} + b^{2} + c^{2}

a^{2} + b^{2} + c^{2} = 21

a b c = 8

(1 - a) (1 - b) (1 - c)

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