Question

1. 25х²-81=0 2. 5/х-3 -8/х - 3 =0

Answer 1

Ответ:

Объяснение:

1. (5х)² - 9² = (5х - 9)(5х + 9) = 0

   1) 5х - 9 = 0   →   5х = 9   →    х₁ = 9/5 = 1,8
   2) 5х + 9 = 0  →   5х = - 9 →    х₂ = -9/5 = -1,8
Ответ: х ₁ = 1,8, х₂ = - 1,8

2. (5/х) - 3 - (8/х) - 3 = 0
   (5/х) - (8/х) = 3 + 3
   (5 - 8)/х = 6
   - 3 = 6х
   6х = -3
    х = -3/6
    х = -1/2 = - 0,5

Answer 2

Let's solve the two equations you've provided:

1. $25x^2 - 81 = 0$

First, let's recognize that this is a quadratic equation in the form of $ax^2 + bx + c = 0$, where $a = 25$, $b = 0$, and $c = -81$.

To solve it, we can use the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

In this case:

$a = 25$ $b = 0$ $c = -81$

Plug these values into the quadratic formula:

$x = \frac{0 \pm \sqrt{0^2 - 4 \cdot 25 \cdot (-81)}}{2 \cdot 25}$

Now, calculate the discriminant (the value inside the square root):

$D = b^2 - 4ac = 0 - 4 \cdot 25 \cdot (-81) = 0 + 8100 = 8100$

Now, plug the discriminant back into the quadratic formula:

$x = \frac{0 \pm \sqrt{8100}}{50}$

Taking the square root of 8100 gives us $x = \pm 90$. So, there are two solutions:

$x_1 = 90$ $x_2 = -90$

2. $\frac{5}{x - 3} - \frac{8}{x} - 3 = 0$

To solve this equation, first, get rid of the fractions by finding a common denominator. The common denominator for $x - 3$ and $x$ is $x(x - 3)$. Multiply both sides of the equation by $x(x - 3)$ to clear the fractions:

$x(x - 3) \cdot \left(\frac{5}{x - 3} - \frac{8}{x} - 3\right) = 0 \cdot x(x - 3)$

Now, simplify the equation:

$5x - 8(x - 3) - 3x(x - 3) = 0$

Expand and simplify further:

$5x - 8x + 24 - 3x^2 + 9x = 0$

Combine like terms:

$-3x^2 + 6x + 24 = 0$

Now, we have a quadratic equation. To solve it, you can use the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

In this case:

$a = -3$ $b = 6$ $c = 24$

Plug these values into the quadratic formula:

$x = \frac{-6 \pm \sqrt{6^2 - 4 \cdot (-3) \cdot 24}}{2 \cdot (-3)}$

Calculate the discriminant:

$D = b^2 - 4ac = 6^2 - 4 \cdot (-3) \cdot 24 = 36 + 288 = 324$

Now, plug the discriminant back into the quadratic formula:

$x = \frac{-6 \pm \sqrt{324}}{-6}$

Taking the square root of 324 gives us $x = \pm 18$. So, there are two solutions:

$x_1 = 18$ $x_2 = -18$