Question

Help me please 2/x²+8/x=2​

Answer 1

Ответ:

2±$\sqrt{5$

Объяснение:

Answer 2

Of course, I'd be happy to help you with this equation! It looks like you have a rational equation that needs to be solved for $x$:

$\frac{2}{x^2} + \frac{8}{x} = 2$.

Let's go through the steps to solve it:

Step 1: Clear the fractions by multiplying both sides of the equation by $x^2$ to get rid of the denominators:

$x^2 \cdot \frac{2}{x^2} + x^2 \cdot \frac{8}{x} = 2 \cdot x^2$.

Simplify:

$2 + 8x = 2x^2$.

Step 2: Rearrange the equation to form a quadratic equation on one side:

$2x^2 - 8x - 2 = 0$.

Step 3: Divide the entire equation by 2 to simplify it:

$x^2 - 4x - 1 = 0$.

Now, this is a quadratic equation. You can solve it using various methods, such as factoring, completing the square, or using the quadratic formula. In this case, the quadratic formula might be the most straightforward:

The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, where $a$, $b$, and $c$ are the coefficients of the quadratic equation $ax^2 + bx + c = 0$.

For your equation $x^2 - 4x - 1 = 0$, the coefficients are $a = 1$, $b = -4$, and $c = -1$.

Plugging the values into the formula:

$x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4 \cdot 1 \cdot (-1)}}{2 \cdot 1}$.

Simplify inside the square root:

$x = \frac{4 \pm \sqrt{16 + 4}}{2}$.

$x = \frac{4 \pm \sqrt{20}}{2}$.

$x = \frac{4 \pm 2\sqrt{5}}{2}$.

Step 4: Simplify the fraction:

$x = 2 \pm \sqrt{5}$.

So, the solutions for the equation $\frac{2}{x^2} + \frac{8}{x} = 2$ are $x = 2 + \sqrt{5}$ and $x = 2 - \sqrt{5}$.

Feel free to double-check my calculations and steps, and let me know if you have any questions!