`(2-3x)/(x)+(2-3y)/(y)+(2-3z)/(z)=0` then `(1)/(x)+(1)/(y)+(1)/(z)=`

If x + y + z = 12, x^(2) + Y^(2) + z^(2) = 96 and (1)/(x)+(1)/(y)+(1)/(z)= 36 . Then find the value x^(3) + y^(3)+z^(3).

If x + y + z = 12, x^(2) + Y^(2) + z^(2) = 96 and (1)/(x)+(1)/(y)+(1)/(z)= 36 . Then find the value x^(3) + y^(3)+z^(3).

If x+y+z=xyz , prove that: a) (3x-x^(3))/(1-3x^(2))+(3y-y^(3))/(1-3y^(2))+(3z-z^(3))/(1-3z^(2))= (3x-x^(3))/(1-3x^(2)).(3y-y^(3))/(1-3y^(2)).(3z-z^(3))/(1-3z^(2)) b) (x+y)/(1-xy) + (y+z)/(1-yz)+(z+x)/(1-zx)= (x+y)/(1-xy) .(y+z)/(1-yz).(z+x)/(1-zx)

If x+y+z=12 and x^(2)+y^(2)+z^(2)=96 and (1)/(x)+(1)/(y)+(1)/(z)=36 then the value x^(3)+y^(3)+z^(3) divisible by prime number is

The value of {(x-y)^3+(y-z)^3+(z-x)^3}/{9(x-y)(y-z)(z-x)} (1) 0 (2) 1/9 (3) 1/3 (4) 1

If x +y+ z=xyz , prove that : (3x-x^3)/(1-3x^2)+ (3y-y^3)/(1-3y^2)+(3z-z^3)/(1-3z^2)= (3x-x^3)/(1-3x^2). (3y-y^3)/(1-3y^2).(3z-z^3)/(1-3z^2) .

If x + y + z = xyz , prove that (3x -x^(3))/ (1-3x^(2)) + (3y -y^(3))/(1- 3y^(2)) +(3z -z^(3))/(1- 3z^(2)) = (3x -x^(3))/(1-3x)^(2) * (3y- y^(3))/(1-3x)^(2)* (3z- z^(3))/(1-3z)^(2) .

If x+y+z=xyz , show that : (3x-x^3)/(1-3x^2) + (3y-y^3)/(1-3y^2) + (3z-z^3)/(1-3z^2) = (3x-x^3)/(1-3x^2) . (3y-y^3)/(1-3y^2) . (3z-z^3)/(1-3z^2)

If x+y+z=xyz , prove that (3x-x^3)/(1-3x^2)+(3y-y^3)/(1-3y^2)+(3z-z^3)/(1-3z^2) = (3x-x^3)/(1-3x^2) cdot(3y-y^3)/(1-3y^2)cdot(3z-z^3)/(1-3z^2)

STATEMENT-1 : The centroid of a tetrahedron with vertices (0, 0,0), (4, 0, 0), (0, -8, 0), (0, 0, 12)is (1, -2, 3). and STATEMENT-2 : The centroid of a triangle with vertices (x_(1), y_(1), z_(1)), (x_(2), y_(2), z_(2)) and (x_(3), y_(3), z_(3)) is ((x_(1)+x_(2)+x_(3))/3, (y_(1)+y_(2)+y_(3))/3, (z_(1)+z_(2)+z_(3))/3)