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+y+z)^2+(a+b+c)^2).`

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 a(y+z)=b(z+x)=c(x+y) then show that (a-b)/(x^(2)-y^(2))=(b-c)/(y^(2)-z^(2))=(c-a)/(z^(2)-x^(2))]

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

If (2y + 2z - x)/a = (2z + 2x - y)/b = (2x + 2y - z)/c ,then show that (9x)/(2b + 2c - a) = (9y)/(2c + 2a - b) = (9z)/(2a + 2b - c)

If a=x-y,b=y-z and c=z-x then the value of a^(3)+b^(3)+c^(3)

If |(a,y,z),(x,b,z),(x,y,c)|=0 , then prove that (a)/(a-x)+(b)/(b-y)+(c)/(c-z)=2

If (a)/(x-a) + (b)/(y-b) + (c )/(z-c)=2 find (x)/(x-a) + (y)/(y-b) + (z)/(z-c) = ?