If a(y+z) = b(z+x) = c(x+y) and out of a, b, c no two of them are equal then show that

Given: a(y+z) = b(z+x) = c(x+y)

Divide all be ‘abc’:

Cancel out the common factor:

Rearrange the terms:

Now, subtract third term from first term, subtract first term from second term and subtract second term from third term and obtain the equivalent:

Solve and cancel the opposite terms:

Hence, proved.