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Differences Of reversed squares MATH HELP!!!?
A mathematician was bored during a long train ride fomr Upstate New York to New York City. Having a little notebook nad pencil always handy, she began to scribble:
21(squared)-12(squared) = 441-144=297
31(squared)-13(squared) = 961-169=792
41(squared)-14(squared)=???
342(squared)-243(squared)=???
1. What is the mathematician invetigating here?
2. Can you find pattern when you continue her investigation for 2 digit or 3 digit numbers? For numbers with any amount of digits?
3. The differences above(297 and 792) are divisible by 99. what ahot the differences of reversed squares for any 2 or 3 digit or any number with any digits?
2 Answers
- Anonymous1 decade agoFavorite Answer
For a 2 digit number xy and it's reverse yx:
(10x + y)² - (10y + x)² =
100x² + 20xy + y² - (100y² + 20xy+ x²) =
99x² - 99y² =
99(x² - y²) =
99(x + y)(x - y)
That does WORK, but I don't know what it proves. Well that's all I've got. I'll think about it.
(21² - 12²) = (21 + 12)(21 - 12) = 33 * 9 = 297
(21² - 12²) = 3²(7² - 4²) = 9 (7 + 4)(7 - 4) = 9 * 11 * 3 = 99 * 3 = 297
It is the difference of two squares, and it does work, but that's not something that needs to be proven.
