WilliamGCash wrote:
I feel like there should be some shortcut here rather than having to do the actual math....
But, what is it? Couldn't really simplify by factoring since 101 is prime. Any ideas here?
This question is testing the following quadratic identity:
x² - y² = (x+y)(x-y)
Thus:
(1001² - 999²)/(101² - 99²)
= (1001+999)(1001-999)/(101+99)(101-99)
= (2000)(2)/(200)(2)
= 10.
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