Exercise 8. Calculate the number

$$
\frac{1000^{2}}{252^{2}-248^{2}}
$$

Only a numerical answer is expected here.
Solution to exercise 8 We use the remarkable identity $a^{2}-b^{2}=(a-b)(a+b)$. Applied to the denominator, this gives

$$
\frac{1000^{2}}{252^{2}-248^{2}}=\frac{1000^{2}}{(252-248)(252+248)}=\frac{1000^{2}}{4 \times 500}=\frac{1000 \cdot 1000}{2 \times 1000}=500
$$