Question : If $x+y+z=19, x y z=216$ and $x y+y z+z x=114$, then the value of $\sqrt{x^3+y^3+z^3+x y z}$ is:

Option 1: 32

Option 2: 30

Option 3: 28

Option 4: 35

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 $x+y+z=10$, $x y+y z+z x=25$ and $x y z=100$, then what is the value of $(x^3+y^3+z^3)$?

Option 1: 450

Option 2: 540

Option 3: 550

Option 4: 570

Question : If $x+y+z=13,x^2+y^2+z^2=133$ and $x^3+y^3+z^3=847$, then the value of $\sqrt[3]{x y z}$ is:

Option 1: $8$

Option 2: $7$

Option 3: $-9$

Option 4: $-6$

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