Question

Не могу сфоткать, надеюсь поймете, решите уравнение пожалуйста очень важно, решается оценка 1) в числителе 5x+14 в знаменателе x^2-4 = в числителе x^2 в знаменателе x^2-4 буду очень благодарен

Answer 1

$\frac{5x+14}{x^2-4} = \frac{x^2}{x^2-4}$

ОДЗ: $x^2 - 4 \neq 0 \\ x \neq 2 \\ x \neq -2$

$\frac{5x+14}{x^2-4} - \frac{x^2}{x^2-4} = 0 \\ \frac{-x^2+5x+14}{x^2-4} =0$

Дробь равна нулю, когда числитель равен нулю 
$-x^2+5x+14 = 0 \\ D = 5^2-4*14*(-1) = 25 + 56 = 81 \\ x_1 = \frac{-5 + \sqrt{81} }{-2} = \frac{4}{-2} = -2$

x1 не соответствует ОДЗ 
$x_2 = \frac{-5 - \sqrt{81} }{-2} = \frac{-14}{-2} = 7$

Ответ: x=7

Если ответ устраивает, то ставьте "Лучшая работа" и Спасибо

Answer 2

Solving the Equation

To solve the equation, we need to find the value of x that satisfies the equation:

$\frac{5x+14}{x^2-4} = \frac{x^2}{x^2-4}$

To begin, let's simplify the equation by multiplying both sides by the common denominator, (x^2-4):

$(5x+14)(x^2-4) = x^2(x^2-4)$

Expanding both sides of the equation:

$5x(x^2-4) + 14(x^2-4) = x^2(x^2-4)$

Simplifying further:

$5x^3 - 20x + 14x^2 - 56 = x^4 - 4x^2$

Rearranging the equation to bring all terms to one side:

$x^4 - 4x^2 - 5x^3 + 14x^2 - 20x + 56 = 0$

Now, we have a fourth-degree polynomial equation. Unfortunately, there is no general formula to solve fourth-degree polynomials. However, we can attempt to factor or use numerical methods to find the solutions.

Since factoring a fourth-degree polynomial can be quite complex, let's use numerical methods to find the approximate solutions.

Numerical Solution

We can use numerical methods, such as graphing or iterative methods like Newton's method, to find the approximate solutions of the equation. However, without specific constraints or additional information, it is challenging to provide an exact solution.

If you have any specific constraints or additional information, please let me know, and I'll be happy to assist you further.