Question : If $x=\sqrt[3]{28}, y=\sqrt[3]{27}$, then the value of $x+y-\frac{1}{x^{2}+xy+y^{2}}$ is:

Option 1: 8

Option 2: 7

Option 3: 6

Option 4: 5

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

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 $x=\frac{\sqrt{5}+1}{\sqrt{5}-1}$ and $y=\frac{\sqrt{5}-1}{\sqrt{5}+1}$, then the value of $\frac{x^{2}+xy+y^{2}}{x^{2}-xy+y^{2}}$ is:

Option 1: $\frac{3}{4}$

Option 2: $\frac{4}{3}$

Option 3: $\frac{3}{5}$

Option 4: $\frac{5}{3}$

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: $mx^3y^3$