Algebra-16 (CAT-2004)

If a/(b+c) = b/(c+a) = c/(a+b) = r, then r can not take any value except__

(1) 1/2      (2) -1     (3) ½ or -1       (4) -1/2 or -1

For Answer Click on "Read more" below:

Solution:

a/(b+c) = b/(c+a) = c/(a+b) = r       

=> a = r(b+c); b = r(c+a); c = r(a+b);

=> a+b+c = r(b+c)+r(c+a)+r(a+b)

=> a+b+c = 2r(a+b+c)

=> (2r-1)(a+b+c) = 0

=> 2r-1 = 0 (or) a+b+c = 0

=> r = ½          --(1)

a+b+c = 0 => b = -(c+a) => b/(c+a) = -1 => r = -1 ---(2)

From (1) and (2), r = ½ or -1

Answer (3)