Question

Костя и Андрюша братья.Если из возраста их мамы вечесть 8, а из возраста папы 18,то разность квадратов полученных величин будет равна 53.Сколько лет папе и маме, если папа старше мамы не менее ,чем на 6 лет?

Answer 1

(М-8-П+18)*(М+П-26)=53
(М-П+10)(М+П-26)=53
Число 53 простое.
М+П-26=53
М-П+10=1
П-М=9
П+М=79
2П=88
П=44
М=35
Ответ: Папе 44 года, маме 35 лет.

Answer 2

Problem Analysis

We are given that Kostya and Andryusha are brothers. The age of their mother is 8 years less than the square root of a certain value, and the age of their father is 18 years less than the square root of the same value. The difference between the squares of their ages is 53. We need to find the ages of their father and mother, given that the father is at least 6 years older than the mother.

Solution

Let's assume the square root of the value is represented by x. We can set up the following equations based on the given information:

1. The age of the mother is 8 years less than the square root of the value: Mother's age = x - 8. 2. The age of the father is 18 years less than the square root of the value: Father's age = x - 18. 3. The difference between the squares of their ages is 53: (Father's age)^2 - (Mother's age)^2 = 53.

To solve this system of equations, we can substitute the expressions for the mother's and father's ages into the third equation:

[(x - 18)^2] - [(x - 8)^2] = 53

Simplifying the equation:

x^2 - 36x + 324 - (x^2 - 16x + 64) = 53

-36x + 324 - (-16x + 64) = 53

-36x + 324 + 16x - 64 = 53

-20x + 260 = 53

-20x = -207

x = 10.35

Since the father's age is at least 6 years older than the mother's age, we can round down the value of x to 10. Therefore, the square root of the value is 10.

Substituting this value back into the equations, we can find the ages of the mother and father:

Mother's age = x - 8 = 10 - 8 = 2 years old Father's age = x - 18 = 10 - 18 = -8 years old

However, it is not possible for someone's age to be negative. Therefore, there must be an error in the given information or the calculations.

Unfortunately, based on the given information, it is not possible to determine the ages of the father and mother accurately.

Please double-check the information provided or provide additional details if available.