Question

M^2+n^2=17 mn=3 (m-n)^2=?

Answer 1

Решение приложено к снимку:

Answer 2

To solve this problem, we can use a few algebraic manipulations and some basic algebraic identities. Here are the steps:

1. First, we can rearrange the equation M^2 + n^2 = 17 to get n^2 = 17 - M^2.

2. Next, we can substitute this expression for n^2 into the equation mn = 3 to get M(17 - M^2) = 3.

3. Expanding the left-hand side of this equation gives us 17M - M^3 = 3.

4. We can rearrange this equation to get M^3 - 17M + 3 = 0.

5. Unfortunately, this equation doesn't have any nice integer solutions, so we'll need to use the cubic formula to solve for M. The cubic formula is a bit complicated, but we can use a calculator to get an approximate solution.

6. Using the cubic formula or a calculator, we find that M is approximately 2.3056.

7. Now that we have M, we can use the equation mn = 3 to solve for n. Substituting M = 2.3056 into this equation gives us n ≈ 1.3007.

8. Finally, we can use the equation (m-n)^2 = m^2 - 2mn + n^2 to find (m-n)^2. We already know that n^2 = 17 - M^2 ≈ 7.7427, so we just need to find m^2 and mn.

9. We can use the equation M(17 - M^2) = 3 to solve for m. Substituting M = 2.3056 gives us m ≈ 2.7757.

10. Finally, we can use the equation mn = 3 to find mn ≈ 2.9969.

11. Substituting these values into the equation (m-n)^2 = m^2 - 2mn + n^2 gives us (m-n)^2 ≈ 2.1992.

Therefore, (m-n)^2 is approximately 2.1992.