If a, b and c represent the lengths of sides of a triangle then the possible integeral value of `(a)/(b+c) + (b)/(c+a) + (c)/(a +b)` is _____

Answer

2

Explanation

`0 lt a lt b + c or (a)/(b+c) lt 1`
`:. (a)/(b+c) + (b)/(c+a) + (c)/(a+b) lt 3`
Also, `[(b+c) + (c+a) + (a+b)] xx [(1)/(b+c) + (1)/(c+a) + (1)/(a+b)] ge 9 " " (A.M. ge H.M.)`
or `(a +b+c) ((1)/(b+c) + (1)/(c+a) + (1)/(a+b)) ge (9)/(2)`
or `(a)/(b+c) + (b)/(c+a) + (c)/(a+b) ge (3)/(2)`
or `(3)/(2) le (a)/(b+c) + (b)/(c+a) + (c)/(a+b) lt 3`
Therefore, integral values of
`(a)/(b+c) + (b)/(c+a) + (c)/(a+b) = 2`