Question

Саша, Андрей и Оля выбрали по натуральному числу. Каждый из них умножил числа, выбранные двумя другими ребятами, на свое число и вычел меньшее произведение из большего. У Саши получилось 1, а у Андрея 121. Сколько могло получиться у Оли? Приведите все возможные варианты и докажите, что других нет.

Answer 1

Ответ:

Антон нннннннннннго

Пошаговое объяснение:

5+9

Answer 2

Problem Analysis

The problem states that Sasha, Andrey, and Olya each chose a natural number. They multiplied the numbers chosen by the other two and subtracted the smaller product from the larger product. Sasha obtained a result of 1, and Andrey obtained a result of 121. We need to determine all possible results that Olya could have obtained and prove that there are no other possibilities.

Solution

Let's assume that Sasha chose the number x, Andrey chose the number y, and Olya chose the number z.

According to the problem, Sasha's result is 1, so we have the equation: xy - yx = 1

Andrey's result is 121, so we have the equation: xy - yx = 121

We can subtract the first equation from the second equation to eliminate the common terms: 121 - 1 = 0

Simplifying, we get: 120 = 0

This is a contradiction because 120 is not equal to 0. Therefore, there are no possible values for Olya's result.

Conclusion

Based on the given information and the analysis above, there are no possible results for Olya. The equations derived from the problem lead to a contradiction, indicating that there is no solution for Olya's result other than an empty set.