Question

{x2- y2=-5. {y=x-1. помогите решить квадратнoe уравнение​ Смотреть ответ Это система уравнений, где одним из элементов является квадратное уравнение? да gavgav3445 gavgav3445 Ответ: Решение представлено на фотографии Спасибо

Answer 1

Solving the System of Equations

The given system of equations is: - Equation 1: x^2 + y^2 = -5 - Equation 2: y = x - 1

To solve the system, we can substitute the expression for y from Equation 2 into Equation 1 and solve for x.

Substituting y = x - 1 into Equation 1 gives: x^2 + (x - 1)^2 = -5

Expanding and simplifying the equation: x^2 + x^2 - 2x + 1 = -5 2x^2 - 2x + 6 = 0

This results in a quadratic equation in terms of x. We can solve for x using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

Where a = 2, b = -2, and c = 6.

Let's calculate the discriminant (b^2 - 4ac) to determine the nature of the solutions.

The discriminant is given by: b^2 - 4ac = (-2)^2 - 4*2*6 = 4 - 48 = -44

Since the discriminant is negative, the solutions for x will be complex numbers.

Solutions for x

Using the quadratic formula: x = (-(-2) ± √(-44)) / (2*2) x = (2 ± 2i√11) / 4 x = (1 ± i√11) / 2

So, the solutions for x are: x = (1 + i√11) / 2 and x = (1 - i√11) / 2

Finding the Corresponding y Values

Now that we have the values for x, we can find the corresponding y values using Equation 2, y = x - 1.

For x = (1 + i√11) / 2: y = (1 + i√11) / 2 - 1 = -1/2 + i√11/2 - 1 = -3/2 + i√11/2

For x = (1 - i√11) / 2: y = (1 - i√11) / 2 - 1 = -1/2 - i√11/2 - 1 = -3/2 - i√11/2

Therefore, the solutions to the system of equations are: x = (1 + i√11) / 2 with y = -3/2 + i√11/2 and x = (1 - i√11) / 2 with y = -3/2 - i√11/2

This completes the solution to the given system of equations. If you have any further questions or need additional assistance, feel free to ask!