Question : If $xy+yz+zx=0$, then $(\frac{1}{x^2–yz}+\frac{1}{y^2–zx}+\frac{1}{z^2–xy})$$(x,y,z \neq 0)$ is equal to:

Option 1: $3$

Option 2: $1$

Option 3: $x+y+z$

Option 4: $0$

Question : If ${x^2+y^2+z^2=2(x+z-1)}$, then the value of $x^3+y^3+z^3$ is equal to:

Option 1: 6

Option 2: 1

Option 3: 2

Option 4: 8

Question : If $x(x+y+z)=20$, $y(x+y+z)=30$, and $z(x+y+z)=50$, then the value of $2(x+y+z)$ is:

Option 1: 20

Option 2: –10

Option 3: 15

Option 4: 18

Question : If $x+y+z=13$ and $x^2+y^2+z^2=69$, then $xy+z(x+y)$ is equal to:

Option 1: 70

Option 2: 40

Option 3: 50

Option 4: 60

Question : If $x, y,$ and $z$ are three sums of money such that y is the simple interest on $x$ and $z$ is the simple interest on $y$ for the same time and at the same rate of interest, then we have:

Option 1: $z^{2}=xy$

Option 2: $xyz=1$

Option 3: $x^{2}=yz$

Option 4: $y^{2}=zx$