Question

Чему равна сумма квадрата разности кубов чисел 3 и 1 и утроенного куба их разности?

Answer 1

Разность кубов чисел 3 и 1 равна 26.
утроенный куб их разности 24.
Следовательно, сумма квадрата равна 600.


Сомневаюсь в павильности решения...

Answer 2

Calculating the Sum of the Square of the Difference of Cubes of 3 and 1 and Triple the Cube of their Difference

To calculate the sum of the square of the difference of cubes of 3 and 1 and triple the cube of their difference, we can follow these steps:

1. Find the Difference of Cubes of 3 and 1: - The difference of cubes of 3 and 1 can be calculated using the formula: \(a^3 - b^3 = (a - b)(a^2 + ab + b^2)\).

2. Square the Difference: - After finding the difference, we can square it to get the square of the difference.

3. Triple the Cube of the Difference: - We then triple the cube of the difference.

Let's calculate each step.

Step 1: Find the Difference of Cubes of 3 and 1

Using the formula \(a^3 - b^3 = (a - b)(a^2 + ab + b^2)\), we can calculate the difference of cubes of 3 and 1: \[3^3 - 1^3 = (3 - 1)(3^2 + 3*1 + 1^2)\]

Step 2: Square the Difference

After finding the difference, we can square it to get the square of the difference.

Step 3: Triple the Cube of the Difference

We then triple the cube of the difference.

Let's calculate the values for each step.

Calculations:

1. Difference of Cubes of 3 and 1: - \(3^3 - 1^3 = (3 - 1)(3^2 + 3*1 + 1^2)\) - \(3^3 - 1^3 = 2(9 + 3 + 1)\) - \(3^3 - 1^3 = 2(13)\) - \(3^3 - 1^3 = 26\)

2. Square of the Difference: - \((3 - 1)^2 = (3 - 1)(3 - 1)\) - \((3 - 1)^2 = 2^2\) - \((3 - 1)^2 = 4\)

3. Triple the Cube of the Difference: - \(3 * (3 - 1)^3 = 3 * 2^3\) - \(3 * (3 - 1)^3 = 3 * 8\) - \(3 * (3 - 1)^3 = 24\)

Final Result:

The sum of the square of the difference of cubes of 3 and 1 and triple the cube of their difference is: \[26 + 4 + 24 = 54\]

Therefore, the sum is 54.