Question : If $x+y+z = 22$ and $xy+yz+zx = 35$, then what is the value of $\small (x-y)^{2}+(y-z)^{2}+(z-x)^{2}$?

Option 1: 793

Option 2: 681

Option 3: 758

Option 4: 715

Question : $x,y,$ 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 $xy+yz+zx$?

Option 1: –1

Option 2: 1

Option 3: 3

Option 4: –3

Question : If $\frac{x^2}{yz}+\frac{y^2}{zx}+\frac{z^2}{xy}=3$, then what is the value of $(x+y+z)^3$?

Option 1: 0

Option 2: 1

Option 3: 2

Option 4: 3

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

Option 1: 2

Option 2: 3

Option 3: 4

Option 4: 1

Question : If $x+y+z=0$, then the value of $\frac{x^2}{yz}+\frac{y^2}{zx}+\frac{z^2}{xy}$ is:

Option 1: 3

Option 2: 1

Option 3: 0

Option 4: 2