Question : If $x+y+z=17, x y z=171$ and $x y+y z+z x=111$, then the value of $\sqrt[3]{\left(x^3+y^3+z^3+x y z\right)}$ is:

Option 1: –64

Option 2: 4

Option 3: 0

Option 4: –4

Question : If $x^2 = y+z$, $y^2=z+x$, $z^2=x+y$, then the value of $\frac{1}{x+1}+\frac{1}{y+1}+\frac{1}{z+1}$ is:

Option 1: –1

Option 2: 1

Option 3: 2

Option 4: 4

Question : What will be the value of $x^{3}+y^{3}+z^{3}-3xyz$, when $x+y+z=9$ and $x^{2}+y^{2}+z^{2}=31?$

Option 1: 27

Option 2: 3

Option 3: 54

Option 4: 9

Question : The value of $\frac{(x-y)^3+(y-z)^3+(z-x)^3}{\left(x^2-y^2\right)^3+\left(y^2-z^2\right)^3+\left(z^2-x^2\right)^3}$, where $x \neq y \neq z$, is:

Option 1: $0$

Option 2: $\frac{1}{(x+y+z)}$

Option 3: $\frac{1}{(x+y)(y+z)(z+x)}$

Option 4: $1$

Question : If $x + y + z = 19, x^2 + y^2 + z^2 = 133$ and $xz = y^2, x > z > 0,$ what is the value of $(x - z)$?

Option 1: 5

Option 2: 0

Option 3: –2

Option 4: –5