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Question 32
If $$\frac{a}{b+c}=\frac{b}{a+c} =\frac{c}{b+a} =r$$, then r cannot take any value except
Solution
a = r(b+c)
b = r(a+c)
c = r(a+b)
On adding all the equations,
a+b+c = 2r(a+b+c)
If r = 1/2, a+b+c = a+b+c (valid)
If r = -1, a+b+c = -2(a+b+c) => a+b+c = 0 => b+c = -a and a/(b+c) = a/(-a) = -1 (valid)
So, r can take the values 1/2 or -1
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