Question

Розв'язати систему рівнянь х^2+y^2=52 x^2-y^2=20 (система)

Answer 1

Складываем оба уравнения:

2x² = 72
x² = 36
x = -6 или x = 6

y² = 52 - x² = 52 - 36 = 16
y = -4 или y = 4

Ответ: (-6; -4); (-6; 4); (6; -4); (6; 4)

Answer 2

Solving the System of Equations

To solve the system of equations x^2 + y^2 = 52 and x^2 - y^2 = 20, we can use the method of substitution or elimination. Let's solve it using the method of substitution.

First, we can solve the second equation for x^2: x^2 = y^2 + 20. Then, we can substitute this expression for x^2 into the first equation.

Substituting x^2 in the First Equation

Substituting x^2 in the first equation, we get: y^2 + 20 + y^2 = 52

Simplifying, we have: 2y^2 = 32 y^2 = 16

Solving for y

Taking the square root of both sides, we get: y = ±4

Finding the Corresponding x Values

Substituting the values of y back into the equation x^2 = y^2 + 20, we can solve for x.

For y = 4: x^2 = 4^2 + 20 x^2 = 36 x = ±6

For y = -4: x^2 = (-4)^2 + 20 x^2 = 36 x = ±6

So, the solutions to the system of equations are: x = 6, y = 4 x = -6, y = 4 x = 6, y = -4 x = -6, y = -4

These are the four pairs of solutions for the given system of equations.