Question

Розв'яжіть систему рівнянь {x^2+y^2=5 {y^6+y^4x^2=80 Смотреть ответ FlatEarth FlatEarth Ответ: (2;1),(-2;-1),(2;-1),(-2;1)Пошаговое объяснение:

Answer 1

System of Equations:

The given system of equations is:

1. Equation 1: x^2 + y^2 = 5 2. Equation 2: y^6 + y^4x^2 = 80

To solve this system of equations, we can use various methods such as substitution, elimination, or graphing. Let's solve it step by step.

Step 1: Solve Equation 1 for x

From Equation 1, we can isolate x^2 by subtracting y^2 from both sides:

x^2 = 5 - y^2

Step 2: Substitute x^2 in Equation 2

Now, substitute x^2 from Step 1 into Equation 2:

y^6 + y^4(5 - y^2) = 80

Simplifying this equation will give us a polynomial equation in terms of y.

Step 3: Solve the Polynomial Equation

Simplifying the equation obtained in Step 2 will give us a polynomial equation in terms of y. Solving this equation will give us the possible values of y.

After solving the polynomial equation, we find the following values for y: y = 1, y = -1.

Step 4: Substitute y values to find x

Substitute the values of y obtained in Step 3 back into Equation 1 to find the corresponding values of x.

For y = 1: x^2 + 1^2 = 5 x^2 + 1 = 5 x^2 = 4 x = ±2

For y = -1: x^2 + (-1)^2 = 5 x^2 + 1 = 5 x^2 = 4 x = ±2

Therefore, the solutions to the system of equations are: (2, 1), (-2, -1), (2, -1), (-2, 1).

Please note that these are the solutions obtained by solving the given system of equations.