Germany | Math Olympiad | Nice Algebra Simplification | (a,b)=?
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- Опубликовано: 12 сен 2024
- How to solve for a and b in this nice Math Olympiad Equation, (a,b) are integers.
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Я делал все проще. Так как в конце получалось 7, а дроби складываются с числителями 5 и 6, то дроби должны давать целое число. То есть для а это 1 или 5. Ну и аходим им подходящее b и проверяем на то целое ли оно число. Все ответ тот же но проверки всего две.
Можно было бы начать с b, но тогда проверки было бы 4 (1,2,3,6). 2 удачных и 2 нет.
A= 5, B= 1 or A= 1, B= 3
Please sir with factors where one is not working so why do we waste time to do for the other factor.
Interger result: a = 5.0, b = 1
Interger result: a = 1.0, b = 3
From simple python script.
If you just start out thinking the 1st denominator is 1, the second denominator is a snap.
IF you say whaf about other possible answers?" I respond "What about them? If I asked you how to get to my next door neighbors house east of me, you'd say; walk ouf your door, and walk east 1 house, and there you are. Duh!! To which I'd reply, 'You could walk west around the block and get there too.' ". Yes you COULD, but why find a different, more complicated route to achieve the same goal? If the 1st answer works, use it. THE PROBLEM DIDN'T ASK FOR. EVERY ANSWER. You supply an answer, the problem is solved.
Там первый знаменатель или 1 или 5. Все остальные дают дробь, и второй дробью ее не убрать пока не дойти до 30. Но там уже при сумме 7 никак не получится.
Поэтому a это однозначно или 1 или 5 или 1 и 5 в зависимости от того можно ли найти для них целую b. Оказалось что можно в обоих случаях.
30 could also be the product of -1 and -30, -30 and -1, -2 and -15, etc. None of these negative cases give valid integer solutions, but they should at least be mentioned. Interestingly if you have (7a-6)(7a-5)=-6.-5 you get the solution a=0, b=0. Not a valid solution because the original equation has 5/a and 6/b and zero division is illegal.
Dari itu 30/7