Question

If `a/(b + c) = b/(c + a) = c/(a + b)`, show that each ratio is equal to `(1)/(2) or -1`.

Answer 1

Now`a/(b + c) = b/(c + a) = c/(a + b)`
= `(a + b + c)/(2(a + b + c)) = (1)/(2)` if a + b + c ≠ 0.
But if a + b + c = 0,   ...(Applying prop. law)
Then `a/(b + c) = a/(-a) = -1`
and `b/(c + a) = b/(-b) = -1`
Also, `c/(a + b) = c/(-c) = -1`.
Hence each of the given ratio is either `(1)/(2) or -1`.