For the following questions answer them individually
If $$x + y + z = 0$$, then what is the value of $$\frac{(3y^2 + x^2 + z^2)}{(2y^2 - xz)}?$$
If $$P = 7 + 4\surd3$$ and $$PQ = 1$$, then what is the value of $$\frac{1}{P^2} + \frac{1}{Q^2}$$?
$$x, y$$ and $$z$$ are real numbers. If $$x^3 + y^3 + z^3 = 13,x + y + z = 1$$ and $$xyz = 1$$, then what is the value of $$xy + yz + zx?$$
If $$\frac{(a + b)}{c} = \frac{6}{5}$$ and $$\frac{(b + c)}{a} = \frac{9}{2}$$, then what is the value of $$\frac{(a + c)}{b}$$?
If $$x^3 + y^3 + z^3 = 3(1 + xyz), P = y + z - x, Q = z + x - y$$ and $$R = x + y - z,$$ then what is the value of $$P^3 + Q^3 + R^3- 3PQR?$$
If $$x_1x_2x_3 = 4(4 + x_1 + x_2 + x_3),$$ then what is the value of $$\left[\frac{1}{(2 + x_1)}\right] + \left[\frac{1}{(2 + x_2)}\right] + \left[\frac{1}{(2 + x_3)}\right]$$?
If $$\alpha$$ and $$\beta$$ are the roots of equation $$x^2 - x + 1 = 0,$$ then which equation will have roots $$\alpha^3$$ and $$\beta^3?$$
