Question

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Critical Question. AAAAA​

Answer 1

Explanation:

abc = 1

We have to prove that,

`(1)/(1+a+b^(-1))+(1)/(1+b+c^(-1))+(1)/(1+c+a^(-1))=1`

We take left hand side of the given equation and solve it,

`(1)/(1+a+(1)/(b))+(1)/(1+b+(1)/(c))+(1)/(1+c+(1)/(a))`

Since, abc = 1,

`(1)/(c)=ab` and c =
`(1)/(ab)`

By substituting these values in the expression,

`(1)/(1+a+(1)/(b))+(1)/(1+b+(1)/(c))+(1)/(1+c+(1)/(a))=(1)/(1+a+(1)/(b))+(1)/(1+b+ab)+(1)/(1+(1)/(ab)+(1)/(a))`

`=(b)/(b+ab+1)+(1)/(1+b+ab)+(ab)/(ab+1+b)`

`=(1+b+ab)/(1+b+ab)`

`=1`

Which equal to the right hand side of the equation.

Hence,
`(1)/(1+a+b^(-1))+(1)/(1+b+c^(-1))+(1)/(1+c+a^(-1))=1`