Предмет: Математика, автор: ulasebla

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Автор ответа: anuapolina08
1

Розв'язання:

Позначимо невідомі числа за a і b, при умові, що (a > b).

Тоді за умовою задачі:

a - b = 6

a²-b² = 84 Розкладемо формулу на множники: (a+b)(a-b) = 84

Підставимо значення (a-b) у формулу:

6(a+b) = 84

a+b = 84/6

a+b = 14

Виразимо значення a:

a = 14-b

Підставимо дане значення у вираз

a-b = 6

(14-b)-b = 6

14-2b = 6

-2b = 6-14.

2b = 8

b = 4.

Знайдемо значення a:

a = 14-b

a = 14-4.

a = 10.

У відповідь необхідно записати добуток a і b:

a·b = 10·4

a·b = 40.

Перевірка:

10-4 = 6

6 = 6

10²-4² = 84

100-16 = 84

84 = 84.

Рівності правильні. Отже, знайдені значення (a = 10 і b = 4) задовольняють умову задачі.

Відповідь: 40.

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