Question

Извлеките квадратный корень из двучлена,представив данное выражение в виде квадрата двучлена:10-2√21;7+2√10;7-√24;3+2√2;4-2√3;7+4√3)подробный ответ

Answer 1

10-2корня из 21 = 100-4*21(возвела всё в квадрат) решила и извлекла из под корня и так с каждым

Answer 2

Finding the Square of the Sum or Difference of Two Numbers

To find the square of the sum or difference of two numbers, we can use the following formulas:

1. Square of the Sum: For two numbers a and b, the square of their sum is given by (a + b)^2 = a^2 + 2ab + b^2. 2. Square of the Difference: For two numbers a and b, the square of their difference is given by (a - b)^2 = a^2 - 2ab + b^2.

Let's apply these formulas to the given expressions.

Calculating the Square of the Sum or Difference

1. For the expression 10 - 2√21: - The square of the difference of 10 and 2√21 is (10 - 2√21)^2 = 100 - 40√21 + 84. - Therefore, the square of 10 - 2√21 is 100 - 40√21 + 84.

2. For the expression 7 + 2√10: - The square of the sum of 7 and 2√10 is (7 + 2√10)^2 = 49 + 28√10 + 40. - Therefore, the square of 7 + 2√10 is 49 + 28√10 + 40.

3. For the expression 7 - √24: - The square of the difference of 7 and √24 is (7 - √24)^2 = 49 - 14√24 + 24. - Therefore, the square of 7 - √24 is 49 - 14√24 + 24.

4. For the expression 3 + 2√2: - The square of the sum of 3 and 2√2 is (3 + 2√2)^2 = 9 + 12√2 + 8. - Therefore, the square of 3 + 2√2 is 9 + 12√2 + 8.

5. For the expression 4 - 2√3: - The square of the difference of 4 and 2√3 is (4 - 2√3)^2 = 16 - 16√3 + 12. - Therefore, the square of 4 - 2√3 is 16 - 16√3 + 12.

6. For the expression 7 + 4√3: - The square of the sum of 7 and 4√3 is (7 + 4√3)^2 = 49 + 56√3 + 48. - Therefore, the square of 7 + 4√3 is 49 + 56√3 + 48.

These are the squares of the given expressions after applying the formulas for the square of the sum or difference of two numbers.