Question

If `x/(b + c - a) = y/(c + a - b) = z/(a + b - c)` then show that (b - c)x + (c - a)y + (a - b) z = 0.

Answer 1

`x/(b + c - a) = y/(c + a - b) = z/(a + b - c)` = k, ...[By k method]
x = (b + xc - a)K,
y = (c + a - b)k,
z = (a + b - c)k
⇒ b² + bc - ab - bc - c² + ca + c² + ca - bc - ab - bc - c² + ca + c² + ab - ac - ab - b² + bc = 0.
Hence proved.