Question : If $xy(x+y)=m$, then the value of $(x^3+y^3+3m)$ is:

Option 1: $\frac{m^3}{xy}$

Option 2: $\frac{m^3}{(x+y)^3}$

Option 3: $\frac{m^3}{x^3y^3}$

Option 4: $mx^3y^3$

Question : If $( x^{3}-y^{3}):( x^{2}+xy+y^{2})=5:1$ and $( x^{2}-y^{2}):(x-y)=7:1$, then the ratio $2x:3y$ equals:

Option 1: $4:1$

Option 2: $2:3$

Option 3: $4:3$

Option 4: $3:2$

Question : If $(x+y)^2=xy+1$ and $x^3-y^3=1$, what is the value of $(x-y)$?

Option 1: 1

Option 2: 0

Option 3: –1

Option 4: 2

Question : If $x$,$y$ and $z$ are real numbers such that $(x-3)^2+(y-4)^2+(z-5)^2=0$, then $(x+y+z)$ is equal to:

Option 1: –12

Option 2: 0

Option 3: 8

Option 4: 12

Question : If $xy = -6$ and $x^3+ y^3= 19$ ($x$ and $y$ are integers), then what is the value of $\frac{1}{x^{–1}}+\frac{1}{y^{–1}}$?

Option 1: –1

Option 2: –2

Option 3: 1

Option 4: 2