Cubic equation related

Algebra Level pending

The system as follows : [ - x + y + z = 1 x+y+z=1 ]; [- x y + y z + z x = 4 xy+yz+zx=4 ]; [- x y z = 4 xyz=4 ]; has 3 unique solutions. What are they

1; -2i; -3i 2; 1i; -4i 1; 4i; -i 1; 2i; -2i

Raffaele Piccirillo by Raffaele Piccirillo , 28, Italy

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1 solution

Using the sostitution x=1-y-z , you get a cubic equation that you can factorize and easily solve

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