25. Given that $x$ and $y$ are positive integers such that $56 \leq x+y \leq 59$ and $0.9<\frac{x}{y}<0.91$, find the value of $y^{2}-x^{2}$.
25. Ans: 177 .
From $0.9 y56$. It follows that $y29.3$. Thus $y=30$ or 31 . If $y=30$, then $27<x<27.3$, no integer value of $x$. If $y=31$, then $27.9<x<28.21$, thus $x=28$. Thus $y^{2}-x^{2}=(31+28)(31-28)=177$.