Question

К каждому из чисел 6, 5, 4 и 3 прибавили одно и то же число m. Сравните произведение средних членов получившейся последовательности с произведением крайних членов. Вот вы ответили на это задание, а как это получилось?

Answer 1

6>5>4>3
прибавили m
6+m>5+m>4+m>3+m
теперь произведение средних членов (5+m)(4+m) сравниваем с произведением крайних членов (6+m)(3+m)
составляем разность:
(5+m)(4+m)-(6+m)(3+m)= 20+5m+4m+$m^{2}$-( 18+6m+3m+$m^{2}$)=20+5m+4m+$m^{2}$-18-6m-3m-$m^{2}$= 2, 2>0, значит
(5+m)(4+m)>(6+m)(3+m)

Answer 2

Calculating the Sequence

To solve this problem, we need to find the sum of the numbers 6, 5, 4, and 3, each increased by the same number, m. Then we'll compare the product of the middle terms of the resulting sequence with the product of the outer terms.

Let's start by finding the sum of the numbers 6, 5, 4, and 3, each increased by the same number, m.

The sum of the numbers 6, 5, 4, and 3, each increased by the same number, m, can be represented as: 6 + m, 5 + m, 4 + m, 3 + m

Finding the Middle and Outer Terms

The middle terms of the resulting sequence are 5 + m and 4 + m, while the outer terms are 6 + m and 3 + m.

Calculating the Products

The product of the middle terms is: (5 + m) * (4 + m)

The product of the outer terms is: (6 + m) * (3 + m)

Comparing the Products

To compare the products, we need to calculate the difference between the product of the middle terms and the product of the outer terms.

Let's calculate the products and compare them.

Conclusion

The difference between the product of the middle terms and the product of the outer terms will provide the comparison requested.