If `a^(2)/(b + c) = b^(2)/(c +a) = c^(2)/(a + b) = 1`, then show that ` 1/(1+a) + 1/(1 + b) + 1/(1+c) = 1`.

Explanation

`a^(2)/(b+c) = 1 or, " a/(b+c) = 1/a` [by componendo process]
` :. 1/(1 + a) = a/(a + b + c) ` ……………..(1)
Similarly , ` 1/(1+b) = b/(a + b + c) ` ………….(2)
and , ` 1/(1 +c) = c/(a + b + c) ` ……………(3)
Now, adding (1), (2) and (3) we get,
`1/(1+a) + 1/(1+b) + 1/(1+c) = a/(a+b+c) + b/(a+b+c) + c/(a + b+c)`
` = (a + b + c)/(a + b + c) = 1`.
` :. 1/(1 + a) + 1/(1 + b) + 1/(1 + c) = 1`.