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Question 9
If $$x + y + z = 2, xy + yz + zx = -11$$ and $$xyz = -12$$, then what is the value of $$\sqrt{x^3 + y^3 + z^3 - 2}$$?
Solution
$$^3 + y^3 + z^3 - 3xyz = (x + y + z)[(x + y + z)^2 - 3(xy + yz +Â zx)]Â $$
$$^3 + y^3 + z^3 - 3(-12) = (2)[(2)^2 - 3(-11)]$$
$$^3 + y^3 + z^3 +36 = (2)[4 + 33]$$
$$^3 + y^3 + z^3Â = 74 - 36$$
$$^3 + y^3 + z^3 - 2Â = 36$$
$$\sqrt{x^3 + y^3 + z^3 - 2}$$ = 6
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