Question

Найдите b если |a|=6 |a+b|=11 и |a-b|=7

Answer 1

Решение задания смотри на фотографии

Answer 2

To find the value of b, let's use the given information and solve the system of equations step by step.

We have three equations:

1. |a| = 6
2. |a + b| = 11
3. |a - b| = 7

Let's start by using the first equation to find the possible values of a.

1. |a| = 6

Since the absolute value of a is 6, a can be either 6 or -6:

• Case 1: a = 6
• Case 2: a = -6

Now let's move on to the second equation and use the cases of a to find the value of b.

2. |a + b| = 11

Case 1: a = 6 |6 + b| = 11

To get the value of b, we need to solve this equation:

|6 + b| = 11

There are two possible solutions for this case:

1. 6 + b = 11, which gives b = 11 - 6 = 5
2. -(6 + b) = 11, which gives b = -(11 + 6) = -17

Case 2: a = -6 |-6 + b| = 11

Again, there are two possible solutions for this case:

1. -6 + b = 11, which gives b = 11 + 6 = 17
2. -(-6 + b) = 11, which gives b = -11 + 6 = -5

Now we have four potential values of b from the two cases:

• b = 5 (when a = 6)
• b = -17 (when a = 6)
• b = 17 (when a = -6)
• b = -5 (when a = -6)

However, there's one more equation left to check:

3. |a - b| = 7

Let's see which combinations of a and b satisfy this equation:

1. When a = 6, b = 5 |6 - 5| = 1 ≠ 7 (doesn't satisfy)

2. When a = 6, b = -17 |6 - (-17)| = 23 ≠ 7 (doesn't satisfy)

3. When a = -6, b = 17 |-6 - 17| = 23 ≠ 7 (doesn't satisfy)

4. When a = -6, b = -5 |-6 - (-5)| = 1 ≠ 7 (doesn't satisfy)

None of the combinations satisfy the third equation. Therefore, there is no solution for b that satisfies all three equations simultaneously.

Please double-check the given equations or let me know if there are any mistakes in the problem statement.