If x^{3} + y^{3} + z^{3} = 3(1 + xyz), P = y + z – x, Q = z + x – y and R = x + y – z, then what is the value of P^{3} + Q^{3} + R^{3}– 3PQR?

P = y + z – x, Q = z + x – y and R = x + y – z And x^{3} + y^{3} + z^{3} = 3(1 + xyz); Suppose x = y = 0 then z^{3} = 3; P = z, Q = z and R = -z; Putting these values in below equation P^{3} + Q^{3} + R^{3} - 3PQR = z^{3} + z^{3} - z^{3} + 3z^{3} => 4z3 Putting z^{3} = 3: P^{3} + Q^{3} + R^{3} - 3PQR = 12

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