Question

x/b+c=y/c+a=z/a+b show that (b-c)x+(c-a)y+(a-b)z

Answer 1

Let x/b+c=y/c+a=z/a+b = kthenx=(b+c)k        ...(1)y=(c+a)k        ...(2)z=(a+b)k        ...(3)to prove(b-c) x+(c-a) y+(a-b) z=0L.H.S. = (b-c) x+(c-a) y+(a-b) z= (b-c) (b+c) k + (c-a) (c+a)k + (a-b) (a+b)k                  by eq (1), (2) & (3)= k [(b-c) (b+c)  + (c-a) (c+a) + (a-b) (a+b) ]=k[b^2 – c^2 + c^2 – a^2 + a^2 – b^2]= k [0]= 0=R.H.S.