Question

Известно, что квадрат суммы выражений 2s и 5 на 40 меньше квадрата их разности. Найди значение s.

Answer 1

Ответ:

${(2s + 5)}^{2} = {(2s - 5)}^{2} - 40 \\ 4 {s}^{2} + 20s + 25 = 4 {s}^{2} - 20s + 25 - 40 \\ 40s = - 40 \\ s = - 1$

Answer 2

Problem Analysis

We are given that the square of the sum of the expressions 2s and 5 is 40 less than the square of their difference. We need to find the value of s.

Solution

Let's break down the problem step by step.

1. The square of the sum of 2s and 5 is given by (2s + 5)^2. 2. The square of their difference is given by (2s - 5)^2. 3. According to the problem, the square of the sum is 40 less than the square of the difference. Mathematically, this can be represented as: (2s + 5)^2 = (2s - 5)^2 - 40.

Now, let's solve this equation to find the value of s.

Expanding both sides of the equation: (2s + 5)^2 = (2s - 5)^2 - 40 Simplifying: 4s^2 + 20s + 25 = 4s^2 - 20s + 25 - 40 Cancelling out the common terms: 20s = -40 Dividing both sides by 20: s = -2

Therefore, the value of s is -2.