Given that \(\begin{align*} \frac{1}{x}+\frac{1}{y}&=5,\\ 3xy+x+y&=4, \end{align*}\) compute \(x^2y+xy^2\).
1/x + 1/y = 5
(x + y) / xy = 5
x + y = 5xy
3xy + x + y = 4
3xy + 5xy = 4
8xy = 4
xy = 4/8 = 1/2
So
x^2 y + xy^2 =
xy ( x + y) =
(1/2) ( 5xy) =
(1/2) ( 5 * (1/2) ) =
5/4
