If `(x+y)/(3a-b) = (y+z)/(3b-c) = (z+x)/(3c-a)`, then show that `(x+y+z)/(a+b+c)= (ax + by+cz)/(a^(2)+b^(2)+c^(2))`

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

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

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

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

If (x)/(a)=(y)/(b)=(z)/(c), then show that (x^(3)+a^(3))/(x^(2)+a^(2))+(y^(3)+b^(3))/(y^(2)+b^(2))+(z^(3)+c^(3))/(z^(2)+c^(2))=((x+y+z)^(3)+(a+b+c)^(2))/((x+b+z)^(2)+(a+b+c)^(2))

If x/a = y/b = z/c , then show that x^(3)/a^(3) + y^(3)/b^(3) + z^(3)/c^(3) = 3 ((x+y+z)/(a+b+c))^(3) .

Show that |a b c a+2x b+2y c+2z x y z|=0

Show that |a b c a+2x b+2y c+2z x y z|=0

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