Question

Сограждане, будьте так добры, подсобите с решением пары примеров. x^4-27x^2+14x+120=0Эта задача уже была на сайте, и предложен такой вариант решения:Разложим на множители:(x-4)*(x-3)*(x+2)*(x+5)=0 x-4=0x1=4 x-3=0 x2=3 x+2=0 x3=-2 x+5=0 x4=-5Я же туповат, и поэтому, не догоняю, каким образом это решалось, поэтому хотелось ы объяснений к этой задаче, и помощь в решении следующей:x^4-71x^2+270x-200=0С подробным описанием каждого действия. Очень надеюсь на Вашу помощь. Заранее спасибо.

Answer 1

В подобных уравнениях корни ищут среди целых делителей свободного члена и проверяют их по схеме Горнера.

Answer 2

Solving the equation x^4 - 27x^2 + 14x + 120 = 0

To solve the equation x^4 - 27x^2 + 14x + 120 = 0, we can follow the steps you mentioned:

1. Factorize the equation: The equation can be factored as (x-4)(x-3)(x+2)(x+5) = 0.

2. Set each factor equal to zero and solve for x: - Setting (x-4) = 0, we get x = 4. - Setting (x-3) = 0, we get x = 3. - Setting (x+2) = 0, we get x = -2. - Setting (x+5) = 0, we get x = -5.

Therefore, the solutions to the equation x^4 - 27x^2 + 14x + 120 = 0 are x = 4, x = 3, x = -2, and x = -5.

Solving the equation x^4 - 71x^2 + 270x - 200 = 0

To solve the equation x^4 - 71x^2 + 270x - 200 = 0, we can follow a similar approach:

1. Factorize the equation: Unfortunately, the equation x^4 - 71x^2 + 270x - 200 = 0 cannot be easily factored using simple integer values. Therefore, we need to use alternative methods to find the solutions.

2. Use the quadratic formula: We can rewrite the equation as a quadratic equation in terms of x^2: (x^2)^2 - 71(x^2) + 270x - 200 = 0.

Let's substitute x^2 with a variable, say y: y^2 - 71y + 270x - 200 = 0.

Now, we can solve this quadratic equation using the quadratic formula: y = (-b ± √(b^2 - 4ac)) / (2a).

In this case, a = 1, b = -71, and c = 270x - 200.

Plugging in these values, we get: y = (-(-71) ± √((-71)^2 - 4(1)(270x - 200))) / (2(1)).

Simplifying further, we have: y = (71 ± √(5041 - 1080x + 800)) / 2.

Now, we need to solve for x. To do that, we substitute y back with x^2: x^2 = (71 ± √(5041 - 1080x + 800)) / 2.

We can solve this equation using numerical methods or approximations.

Unfortunately, without additional information or constraints, it is difficult to provide an exact solution for the equation x^4 - 71x^2 + 270x - 200 = 0. However, you can use numerical methods such as graphing, factoring, or iterative methods to approximate the solutions.