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

Question : If $x$ and $y$ are real numbers, then the least possible value of $4 (x -2)^2+ (y-3)^2-2 (x-3)^2$ is:

Option 1: 3

Option 2: –4

Option 3: 1

Option 4: –8

Question : If $x + y + z = 19, x^2 + y^2 + z^2 = 133$ and $xz = y^2, x > z > 0,$ what is the value of $(x - z)$?

Option 1: 5

Option 2: 0

Option 3: –2

Option 4: –5

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 $x^2 = y+z$, $y^2=z+x$, $z^2=x+y$, 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