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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If $$\frac{a}{b+c}=\frac{b}{a+c} =\frac{c}{b+a} =r$$, then r cannot take any value except

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