Question : If $a^{2}+b^{2}+c^{2}-ab-bc-ca=0$, then

Option 1: $a=b=c$

Option 2: $a\neq b=c$

Option 3: $a=b\neq c$

Option 4: $a\neq b\neq c$

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 – 8)² – (x + 8)² = 0. What is the value of x?

Option 1: 1

Option 2: 32

Option 3: 0

Option 4: –32

Question : If $x+\frac{1}{x}=0$, then the value of $x^{5}+\frac{1}{x^{5}}$ is:

Option 1: 2

Option 2:  –1

Option 3: 1

Option 4: 0

Question : If $a+b+c=0$ and $a^2+b^2+c^2=40$, then what is the value of $a b+b c+c a$?

Option 1: –30

Option 2: –20

Option 3: –25

Option 4: –40