Question

ПОМОГИТЕ РЕШИТЬ СИСТЕМУ УРАВНЕНИЙ х - у = 10 ху = -21

Answer 1

Ответ:

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Answer 2

Solving the System of Equations:

To solve the system of equations x - y = 10 and xy = -21, we can use the substitution method. First, let's solve for one variable in terms of the other using the second equation.

From the second equation xy = -21, we can express y in terms of x as y = -21/x.

Now, we can substitute this expression for y into the first equation x - y = 10 to solve for x.

Substituting y = -21/x into x - y = 10 gives us x - (-21/x) = 10.

Multiplying through by x to clear the fraction, we get x^2 + 21 = 10x.

This simplifies to the quadratic equation x^2 - 10x + 21 = 0.

We can solve this quadratic equation to find the values of x and then use these values to find the corresponding values of y.

Quadratic Equation Solution:

Using the quadratic formula x = (-b ± √(b^2 - 4ac)) / (2a), where a = 1, b = -10, and c = 21, we can find the solutions for x.

The discriminant Δ = b^2 - 4ac is (-10)^2 - 4*1*21 = 100 - 84 = 16.

So, the solutions for x are x = (10 ± √16) / 2.

This gives us x = (10 ± 4) / 2, which simplifies to x = 7 and x = 3.

Finding the Corresponding Values of y:

Now that we have the values of x, we can find the corresponding values of y using the equation y = -21/x.

For x = 7, y = -21/7 = -3.

For x = 3, y = -21/3 = -7.

Therefore, the solutions to the system of equations are (x, y) = (7, -3) and (x, y) = (3, -7).

These are the two sets of values for x and y that satisfy both equations simultaneously.

I hope this helps! If you have any further questions, feel free to ask.