Question

X-y=1 x^3-y^3=7 решите систему уравнений

Answer 1

Ответ:

Незачто

Объяснение:

Answer 2

To solve the system of equations:

1. x - y = 1 ...(Equation 1)
2. x^3 - y^3 = 7 ...(Equation 2)

We can start by using Equation 1 to solve for one variable in terms of the other. Then, we can substitute this value into Equation 2 to find the value of the remaining variable.

Step 1: Solve Equation 1 for x in terms of y: x = y + 1

Step 2: Substitute the value of x from Step 1 into Equation 2: (y + 1)^3 - y^3 = 7

Now, expand the left side of the equation: (y + 1)^3 = (y + 1)(y + 1)(y + 1) = (y^2 + 2y + 1)(y + 1) = y^3 + 3y^2 + 3y + 1

Now, our equation becomes: y^3 + 3y^2 + 3y + 1 - y^3 = 7

Simplify the equation: 3y^2 + 3y - 6 = 0

Step 3: Divide the equation by 3 to simplify further: y^2 + y - 2 = 0

Step 4: Factor the quadratic equation: (y + 2)(y - 1) = 0

Now, set each factor equal to zero and solve for y:

1. y + 2 = 0 y = -2

2. y - 1 = 0 y = 1

Now that we have found the possible values of y, we can find the corresponding values of x using Equation 1:

For y = -2: x = y + 1 x = -2 + 1 x = -1

For y = 1: x = y + 1 x = 1 + 1 x = 2

So, the solutions to the system of equations are: x = -1, y = -2 x = 2, y = 1