Question : If $999x+888y=1332$ and $888x+999y=555$, then the value of $x+y$ is:

Option 1: 888

Option 2: 555

Option 3: 1

Option 4: 999

Question : If $\frac{x}{y}+\frac{y}{x}=1$ and $x+y=2$, then the value of $x^3+y^3$ is:

Option 1: 1

Option 2: 3

Option 3: 0

Option 4: 2

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 : If $x^4+y^4=x^2 y^2$, then the value of $x^6+y^6$ is:

Option 1: 2

Option 2: 0

Option 3: 1

Option 4: 3

Question : If $x^4+x^2 y^2+y^4=133$ and $x^2-x y+y^2=7$, then what is the value of $xy$?

Option 1: 8

Option 2: 12

Option 3: 4

Option 4: 6

Question : If $x^4+x^2 y^2+y^4=21$ and $x^2+xy+y^2=3$, then what is the value of $4xy $?
 

Option 1: –8

Option 2: 4

Option 3: –4

Option 4: 12