$x^{3} + y^{3} + z^{3} - 3 x y z \geq (x + y + z) (x^{2} + y^{2} + z^{2} - x y - y z - z x)$ .
State whether the above statement is true or false.

True

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False

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Solution

The correct option is A True
We know that, $x^{3} + y^{3} + z^{3} - 3 x y z = (x + y + z) (x^{2} + y^{2} + z^{2} - x y - y z - z x)$ .
Since it is given $\geq$ in which equality symbol exists, the statement is true.

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