Question

if x/(b+c)=y/(c+a)=z/(a+b) then
1)(x-y)/(b-a)=(y-z)/(c-b)=(z-x)/(a-c)
2)none of this is true
3)x/a=y/b=z/c
4)(x-y)/c=(y-z)/b=(z-x)/c​

Answer 1

Step-by-step explanation:

xb+c=yc+a=za+b=k (say) xb+c=yc+a=za+b=k (say)

⟹x=k(b+c);y=k(c+a);z=k(a+b)⟹x=k(b+c);y=k(c+a);z=k(a+b)

LHS=(b−c)x+(c−a)y+(a−b)zLHS=(b−c)x+(c−a)y+(a−b)z

=(b−c)k(b+c)+(c−a)k(c+a)+(a−b)k(a+b)=(b−c)k(b+c)+(c−a)k(c+a)+(a−b)k(a+b)

=k[(b2−c2)+(c2−a2)+(a2−b2)]=0=RHS=k[(b2−c2)+(c2−a2)+(a2−b2)]=0=RHS

PROVED