If x = y = 333 and z = 334,then the value of | vedclass

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(C) The algebraic identity for $x^{3} + y^{3} + z^{3} - 3xyz$ is given by:$x^{3} + y^{3} + z^{3} - 3xyz = \frac{1}{2}(x + y + z)[(x - y)^{2} + (y - z)

Vedclass · Accepted Answer

$1000$

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(C) The algebraic identity for $x^{3} + y^{3} + z^{3} - 3xyz$ is given by:$x^{3} + y^{3} + z^{3} - 3xyz = \frac{1}{2}(x + y + z)[(x - y)^{2} + (y - z)^{2} + (z - x)^{2}]$Given $x = 333$,$y = 333$,and $z = 334$:Sum $(x + y + z) = 333 + 333 + 334 = 1000$Differences:$(x - y) = 333 - 333 = 0$$(y - z) = 333 - 334 = -1$$(z - x) = 334 - 333 = 1$Substituting these values into the identity:$= \frac{1}{2}(1000)[(0)^{2} + (-1)^{2} + (1)^{2}]$$= \frac{1}{2}(1000)[0 + 1 + 1]$$= \frac{1}{2}(1000)(2) = 1000$

If $x = y = 333$ and $z = 334$,then the value of $x^{3} + y^{3} + z^{3} - 3xyz$ is

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