Problem: 100022522−2482\dfrac{1000^{2}}{252^{2}-248^{2}}2522−248210002 equals
Answer Choices:
A. 62,50062,50062,500
B. 100010001000
C. 500500500
D. 250250250
E. 12\dfrac{1}{2}21
Solution:
100022522−2482=1000⋅1000(252+248)(252−248)=1000500⋅10004=500.\begin{aligned} \dfrac{1000^{2}}{252^{2}-248^{2}}&=\dfrac{1000 \cdot 1000}{(252+248)(252-248)} \\ &=\dfrac{1000}{500} \cdot \dfrac{1000}{4}=500 . \end{aligned} 2522−248210002=(252+248)(252−248)1000⋅1000=5001000⋅41000=500.