If $x+y=2$ and $\frac{1}{x}+\frac{1}{y}=\frac{18}{5}$, then the value of $\left(x^3+y^3\right)$ is:

$4 \frac{2}{3}$

If $x+y=2$ 

$\frac{1}{x}+\frac{1}{y}=\frac{18}{5}$

$\frac{x + y}{xy}=\frac{18}{5}$

$\frac{2}{xy}=\frac{18}{5}$

xy = $\frac{5}{9}$

The value of $\left(x^3+y^3\right)$ = 

If x + y  = n

then, $x^3 + y^3$ = n³ - 3 × n × xy

$x^3 + y^3$ = 2³ - 3 × 2 × $\frac{5}{9}$

= $x^3 + y^3$ = 8 - $\frac{10}{3}$

$x^3 + y^3$ = $4 \frac{2}{3}$