Question

Решите уравнение через теорему Витта х^2-8x+13=0

Answer 1

Х₁+х₂=8
х₁*х₂=13
решать лень, но х₁=4+√3;  х₂=4-√3

Answer 2

Solving the Equation using the Vieta's Theorem

To solve the equation x^2 - 8x + 13 = 0 using Vieta's Theorem, we can use the following approach:

1. Identify the Coefficients: The given quadratic equation is in the form of x^2 + bx + c = 0. From the equation x^2 - 8x + 13 = 0, we can identify that b = -8 and c = 13.

2. Apply Vieta's Formulas: Vieta's formulas state that for a quadratic equation ax^2 + bx + c = 0, the sum of the roots is -b/a and the product of the roots is c/a.

3. Calculate the Sum and Product of the Roots: Using the identified coefficients, we can calculate the sum and product of the roots.

- The sum of the roots, denoted as S, is given by S = -b/a. - The product of the roots, denoted as P, is given by P = c/a.

4. Find the Roots: Once we have the sum and product of the roots, we can solve for the roots of the quadratic equation.

Let's proceed with the calculations.

Calculation

1. Identify the Coefficients: - From the equation x^2 - 8x + 13 = 0, we have: - b = -8 - c = 13

2. Apply Vieta's Formulas: - The sum of the roots, S, is given by S = -b/a. - The product of the roots, P, is given by P = c/a.

Using the given values: - S = -(-8)/1 = 8 - P = 13/1 = 13

3. Find the Roots: - The roots of the quadratic equation can be found using the sum and product of the roots.

Conclusion

Using Vieta's Theorem, we have calculated the sum and product of the roots of the given quadratic equation x^2 - 8x + 13 = 0. The sum of the roots is 8 and the product of the roots is 13. These values can be used to find the actual roots of the equation.