UPSKILL MATH PLUS

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(i) Verify that: x^3 + y^3 + z^3 – 3xyz  = \frac{1}{2} (x + y + z) [(x – y)^2 + (y – z)^2 + (z – x)^2]
 
(ii) If x + y + z = 0, show that x^3 + y^3 + z^3 = 3xyz.
 
Important!
This is a creative exercise. It will be checked manually by the teacher.