Question

X2 + y2 = 18,xy = 9​

Answer 1

Ответ:

Объяснение:

x = y = 3

x = y = -3

9 раскладывается только на  3*3 или (-3)(-3)

(± 3)² + (±3)² = 18

Answer 2

The equations you've provided are:

1. $x^2 + y^2 = 18$
2. $xy = 9$

These equations represent a system of two non-linear equations with two variables, $x$ and $y$. To solve this system, you can use substitution or elimination methods. Here's one way to solve it using the substitution method:

From equation 2, we can express $y$ in terms of $x$:

$y = \frac{9}{x}$

Now, substitute this expression for $y$ into equation 1:

$x^2 + \left(\frac{9}{x}\right)^2 = 18$

Now, simplify this equation:

$x^2 + \frac{81}{x^2} = 18$

Multiply both sides of the equation by $x^2$ to get rid of the fraction:

$x^4 + 81 = 18x^2$

Now, move all terms to one side of the equation:

$x^4 - 18x^2 + 81 = 0$

This is a quadratic equation in terms of $x^2$. Let's make a substitution:

Let $u = x^2$, so the equation becomes:

$u^2 - 18u + 81 = 0$

Now, solve this quadratic equation for $u$. You can factor it:

$(u - 9)(u - 9) = 0$

This gives us a repeated root:

$u = 9$

Now, substitute back for $x^2$:

$x^2 = 9$

Take the square root of both sides:

$x = \pm 3$

Now that we have the values of $x$, we can find the corresponding values of $y$ using equation 2:

For $x = 3$: $y = \frac{9}{3} = 3$

For $x = -3$: $y = \frac{9}{-3} = -3$

So, the solutions to the system of equations are:

1. $x = 3$ and $y = 3$
2. $x = -3$ and $y = -3$