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:
Answer & explanation
Correct answer: option 1
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 - $\frac{10}{3}$
$x^3 + y^3$ = $4 \frac{2}{3}$