Question

X^2+y^2=100 (x-7y)(x+7y)=0Решить систему

Answer 1

Решение во вложении:

Answer 2

To solve the system of equations, we need to find the values of x and y that satisfy both equations:

1. x^2 + y^2 = 100
2. (x - 7y)(x + 7y) = 0

Let's start solving the system step by step:

Step 1: (x - 7y)(x + 7y) = 0

The equation (x - 7y)(x + 7y) = 0 implies that either (x - 7y) = 0 or (x + 7y) = 0 or both must be true. So we get two cases to consider:

Case 1: x - 7y = 0 Solving for x, we get: x = 7y

Case 2: x + 7y = 0 Solving for x, we get: x = -7y

Step 2: Substitute the values of x from Case 1 and Case 2 into the first equation (x^2 + y^2 = 100) and solve for y.

Case 1: x = 7y (7y)^2 + y^2 = 100 49y^2 + y^2 = 100 50y^2 = 100 y^2 = 100/50 y^2 = 2 y = ±√2

So we get two values of y: y = √2 and y = -√2.

Step 3: Find the corresponding values of x for each value of y.

For y = √2: x = 7y x = 7√2

For y = -√2: x = 7y x = 7(-√2)

So, the solutions to the system of equations are:

1. x = 7√2 and y = √2
2. x = -7√2 and y = -√2