InterviewSolution
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InterviewSolution
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a b c = 1 , \text { show that } \frac { 1 } { 1 + a + b ^ { - 1 } } + \frac { 1 } { 1 + b + c ^ { - 1 } } + \frac { 1 } { 1 + c + a ^ { - 1 } } = 1 |
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Answer» abc=1 ⟹c=1/ab 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/(1+b+ab)+1/(1+b+ab)+ab/(1+b+ab) =1+b+ab/(1+b+ab) =1 |
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