Given that \begin{align*} \frac{1}{x}+\frac{1}{y}&=3,\\ xy+x+y&=4, \end{align*} compute $x^2y+xy^2$.
1/x + 1/y = 3 → (x + y) / xy = 3 → x + y = 3xy
So
xy + ( x + y) = 4
xy + 3xy = 4
4xy = 4
xy = 1
x^2y + xy^2 =
xy ( x + y) =
1 ( 3xy) =
1 ( 3 * 1) =
3
+230 
