24. When 15 is added to a number $x$, it becomes a square number. When 74 is subtracted from $x$, the result is again a square number. Find the number $x$.
24. Ans: 2010.
Let $15+x=m^{2}$ and $x-74=n^{2}$. We have $m^{2}-n^{2}=89=1 \times 89 .(m-n)(m+n)=1 \times 89$. Let $m-n=1$ and $m+n=89$. Solving $m=45$ and $n=44$. Thus the number $x$ is $45^{2}-15=2010$.