Question

У исполнителя Квадратор две команды, которым присвоены номера: 1. возведи в квадрат 2. вычти y Первая из них возводит число на экране во вторую степень, вторая уменьшает число на y. Исполнитель работает только с натуральными числами. Известно, что алгоритм 11221 переводит число 2 к числу 64. Определите значение y

Answer 1

Ответ:

y=4

Объяснение:

Команда    Результат

1                         4

1                         16

2                         16-y

2                         16-2y

1                          (16-2y)^2

итоговый результат (16-2y)^2=64

256+4y^2-64y=64

4y^2-64y+192=0

y^2-16y+48=0

16-2y>0  y<8

y=12  не удовлетворяет ОДЗ

y=4

Answer 2

Problem Analysis

We are given that there are two commands assigned to the performer "Quadrator": 1. "Square" command: It squares the number on the screen. 2. "Subtract" command: It subtracts a value "y" from the number on the screen.

We are also given that the algorithm 11221 converts the number 2 to 64. We need to determine the value of "y".

Solution

To solve this problem, we need to reverse engineer the algorithm 11221 to find the value of "y". Let's analyze the algorithm step by step:

1. The algorithm starts with the number 2. 2. The first command, "Square", squares the number on the screen. So, after this step, the number becomes 2^2 = 4. 3. The second command, "Subtract", subtracts a value "y" from the number on the screen. Let's assume the value of "y" is "a" at this point. So, after this step, the number becomes 4 - a. 4. The third command, "Square", squares the number on the screen again. So, after this step, the number becomes (4 - a)^2. 5. The fourth command, "Square", squares the number on the screen one more time. So, after this step, the number becomes [(4 - a)^2]^2 = (4 - a)^4. 6. The fifth command, "Subtract", subtracts a value "y" from the number on the screen. Let's assume the value of "y" is "b" at this point. So, after this step, the number becomes (4 - a)^4 - b.

According to the given information, the algorithm 11221 converts the number 2 to 64. Therefore, we can set up the following equation:

(4 - a)^4 - b = 64

Now, we need to solve this equation to find the values of "a" and "b".

Solving the Equation

Let's solve the equation (4 - a)^4 - b = 64 step by step:

1. Expand the fourth power: (4 - a)^4 = (4 - a)(4 - a)(4 - a)(4 - a) 2. Simplify the expression: (4 - a)(4 - a)(4 - a)(4 - a) = (4 - a)^2 * (4 - a)^2 = (16 - 8a + a^2) * (16 - 8a + a^2) 3. Multiply the expressions: (16 - 8a + a^2) * (16 - 8a + a^2) = 256 - 128a + 16a^2 - 128a + 64a^2 - 8a^3 + 16a^2 - 8a^3 + a^4 4. Simplify the expression: 256 - 256a + 48a^2 - 16a^3 + a^4 5. Substitute the expression into the equation: (256 - 256a + 48a^2 - 16a^3 + a^4) - b = 64 6. Rearrange the equation: a^4 - 16a^3 + 48a^2 - 256a + (192 - b) = 0

Now, we have a quartic equation in terms of "a". To solve this equation, we can use numerical methods or approximation techniques. However, without additional information or constraints, it is not possible to determine the exact values of "a" and "b".

Therefore, the value of "y" cannot be determined with the given information.

Conclusion

Based on the given information and the analysis performed, the value of "y" cannot be determined. Additional information or constraints are required to solve the equation and find the values of "a" and "b".