Question

Сумма двух чисел равна 22, а разность квадратов этих чисел равна 176. Что это за числа?

Answer 1

А + В = 22, откуда B = 22-A 
А^2 - В^2 = 176 
Вместо В подставляем его значение чере А 
A^2 - (22-A)^2 = 176 
A^2 - (484 - 44A + A^2) = 176 
44A = 308 
A = 7 
В = 22 - А = 22 - 7 = 15

Answer 2

Problem Analysis

We are given two pieces of information: 1. The sum of two numbers is 22. 2. The difference between the squares of these numbers is 176.

Let's assume the two numbers are x and y.

Equations

Based on the given information, we can form the following equations: 1. x + y = 22 (Equation 1) 2. x^2 - y^2 = 176 (Equation 2)

Solving the Equations

To find the values of x and y, we can solve these equations simultaneously.

From Equation 1, we can express x in terms of y: x = 22 - y

Substituting this value of x into Equation 2, we get: (22 - y)^2 - y^2 = 176

Expanding and simplifying the equation: 484 - 44y + y^2 - y^2 = 176

Simplifying further: 44y = 484 - 176 44y = 308 y = 308 / 44 y = 7

Substituting the value of y back into Equation 1, we can find x: x = 22 - 7 x = 15

Therefore, the two numbers are 15 and 7.

Answer

The two numbers that satisfy the given conditions are 15 and 7.