In the expansion of $(x+y)^{n}$ using the binomial theorem, the second term is 240, the third term is 720, and the fourth term is 1080. Find $x, y$, and $n$.

#
Given the conditions $n x^{n-1} y=240, n(n-1) x^{n-2} y^{2}=2 \cdot 720, n(n-1)(n-2) x^{n-3} y^{3}=6 \cdot 1080$. By dividing the second equation by the first, and the third by the second, and denoting

$t=y / x$, we get $(n-1) t=6,(n-2) t=4.5$. From this, $t=1.5, n-1=4$. Substituting into the first equation: $5 x^{5} \cdot 1.5=$ 240, that is, $x=2$, and $y=3$.

## Answer

$x=2, y=3, n=5$.