Verify that ` x ^(3) + y ^(3) + z ^(3) - 3xyz =1/2 (x + y + z) [(x-y)^(2) + (y-z) ^(2) + (z-x) ^(2) ]`

(x-y)^(3)+(y-z)^(3)+(z-x)^(3)

Let's write the value of x^3 - y^3 -z^3 - 3xyz if x = y + z

((x-y)^(3)+(y-z)^(3)+(z-x)^(3))/((x-y)(y-z)(z-x))=

If x^((1)/(3)) + y^((1)/(3)) + z^((1)/(3)) = 0 , then prove that (x + y + z)^(2) = 27 xyz

If x + y + z = 0 , then prove that x^(3)+y^(3)+z^(3)= 3xyz

The three adjacent surfaces of cuboid are x sq. unit, y sq. unit and z sq. unit. The length of its one of the diagonal is Option 1 (xy/z+yz/x+zx/y)^(1/2) Option 2 ( z x/ y + x y/ z + y z/ x )^(1/2) Option 3 ( x y/ z + y z/ x + z x/ y ) Option 4 ( z y/ x + y z/ x + x y/ z )

Factorise : x(y-z)^(2)+y(z-x)^(2)+z(x-y)^(2)+8xyz

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

If x/y = y/z , then simplify (xyz ( x + y + z)^(3))/((xy+yz+zx)^(3)) .

Solve the following system of equations by matrix inversion method: (2)/(x) + (3)/(y) - (4)/(z) = -3, (1)/(x) + (2)/(y) + (6)/(z) = 2, (3)/(x)-(1)/(y)+(2)/(z) = 5