Question

If x+ y + z= 1, xy + yz + zx = -1 and xyz =-1 then what is the value of x^3 + y^3 + Z^3

Answer 1

${x}^{3} + {y}^{3} + {z}^{3} - 3xyz = 0 \\ {x}^{3} + {y}^{3} + {z}^{3} = 3xyz \\ {x}^{3} + {y}^{3} + {z}^{3} = 3 \times 1(xyz = 1 \: given) \\ {x}^{3} + {y}^{3} + {z}^{3} = 3$
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