If  x + y + z  =  1, xy + yz + zx  =  −1  and  xyz  =  −1 , the value of  x3 + y3 + z3  = Select an answerA1B2C4D–1

The solution to this problem can be found by using the formula for the sum of cubes, which is a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca).

Given that x + y + z = 1, xy + yz + zx = -1, and xyz = -1, we can substitute these values into the formula.

First, we need to find the value of x^2 + y^2 + z^2. We can do this by squaring the equation x + y + z = 1 to get x^2 + y^2 + z^2 + 2(xy + yz + zx) = 1.

Substituting the value of xy + yz + zx = -1 into this equation gives us x^2 + y^2 + z^2 - 2 = 1, so x^2 + y^2 + z^2 = 3.

Now we can substitute x + y + z = 1, x^2 + y^2 + z^2 = 3, and xy + yz + zx = -1 into the formula for the sum of cubes to get x^3 + y^3 + z^3 - 3(-1) = (1)(3 - (-1)).

Solving this equation gives us x^3 + y^3 + z^3 + 3 = 4, so x^3 + y^3 + z^3 = 4 - 3 = 1.

Therefore, the value of x^3 + y^3 + z^3 is 1, so the correct answer is A1.