Question

Даны три числа, из которых каждое следующее на 7 больше предыдущего. Найти эти число, если произведение двух крайних чисел на 56 больше произведения меньшего и среднего числа. Завтра контрольная, а я вообще не понимаю как решать? За рание спасибо!

Answer 1

Problem Analysis

To solve this problem, we are given three numbers, where each subsequent number is 7 greater than the previous one. We need to find these numbers, given that the product of the two outer numbers is 56 greater than the product of the smaller and middle numbers.

Let's break down the problem step by step.

Step 1: Define the numbers

Let's assume the three numbers are x, x+7, and x+14. Here, x represents the first number, x+7 represents the second number, and x+14 represents the third number.

Step 2: Formulate the equation

According to the problem statement, the product of the two outer numbers (x and x+14) is 56 greater than the product of the smaller and middle numbers (x+7).

Mathematically, we can represent this as:

(x)(x+14) = (x+7)(x+7) + 56

Step 3: Solve the equation

Let's solve the equation to find the value of x.

Expanding the equation, we get:

x^2 + 14x = x^2 + 14x + 49 + 56

Simplifying the equation, we have:

x^2 + 14x = x^2 + 14x + 105

Subtracting x^2 + 14x from both sides, we get:

0 = 105

This equation has no solution, which means there are no values of x that satisfy the given conditions. Therefore, there are no numbers that meet the given criteria.

Conclusion

Based on the analysis, there are no three numbers that satisfy the given conditions.