Question

К каждому из чисел 4,5,6,7 прибавили одно и тоже действительное число а.Сравните произведение средних членов получившейся последовательности с произведением крайних.ПОМОГИТЕ ПАЖАЛУСТА СРОЧНО!!!!​

Answer 1

добавили х...

получили:

4+х

5+х

6+х

7+х

сравним

(4+х)(7+х) и (5+х)(6+х).

(4+х)(7+х)=28+11х+х²

(5+х)(6+х)=30+11х+х²

мы видим, что произведение средних членов

больше произведения крайних на 2

Answer 2

#### Problem Analysis We are given the numbers 4, 5, 6, and 7, and we need to add the same real number 'a' to each of them. We are asked to compare the product of the middle terms of the resulting sequence with the product of the outer terms. #### Solution To solve this problem, let's first find the resulting sequence after adding 'a' to each number. The given numbers are: 4, 5, 6, 7 After adding 'a' to each number, the resulting sequence is: 4 + a, 5 + a, 6 + a, 7 + a Now, let's calculate the product of the middle terms and the product of the outer terms. Product of the middle terms: (5 + a) * (6 + a) Product of the outer terms: (4 + a) * (7 + a) To compare these two products, we can expand the expressions and simplify them. Product of the middle terms: (5 + a) * (6 + a) = 30 + 11a + a^2 Product of the outer terms: (4 + a) * (7 + a) = 28 + 11a + a^2 As we can see, the product of the middle terms and the product of the outer terms are the same: 30 + 11a + a^2. Therefore, the product of the middle terms of the resulting sequence is equal to the product of the outer terms. #### Answer The product of the middle terms of the resulting sequence, after adding the same real number 'a' to each of the numbers 4, 5, 6, and 7, is equal to the product of the outer terms. The expression for both products is 30 + 11a + a^2. I hope this helps! Let me know if you have any further questions.