Question

При каких значениях х значение функции у =5х+2/х^2-х-2=1?

Answer 1

Ответ:

Пошаговое объяснение:

5х+2/ (х²-х-2)=1.

5х+2=х²-х-2.

х²-6х-4=0.

х₁₂=3±√(9+4).

х₁=3+√13.

х₂=3-√13.

При этих значениях    х.   (если правильно записан пример).

Answer 2

To find the values of x for which the function y = (5x + 2)/(x^2 - x - 2) is equal to 1, we simply set y equal to 1 and solve for x.

So, we have:

1 = (5x + 2)/(x^2 - x - 2)

To make solving this equation easier, let's first factor the denominator (x^2 - x - 2) as follows:

x^2 - x - 2 = (x - 2)(x + 1)

Now, the equation becomes:

1 = (5x + 2)/[(x - 2)(x + 1)]

Next, we can multiply both sides of the equation by the denominator to get rid of the fraction:

1 * (x - 2)(x + 1) = 5x + 2

Expand the left side:

(x - 2)(x + 1) = 5x + 2

Now, expand further:

x^2 - x + x - 2 = 5x + 2

Combine like terms:

x^2 - 2 = 5x + 2

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

x^2 - 5x - 2 - 2 = 0

x^2 - 5x - 4 = 0

To solve this quadratic equation, we can use factoring or the quadratic formula. Factoring this particular equation may not be straightforward, so let's use the quadratic formula:

The quadratic formula states that for an equation in the form of ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac)) / 2a

In our case, a = 1, b = -5, and c = -4. Plug these values into the formula:

x = [5 ± √((-5)^2 - 4 * 1 * (-4))] / 2 * 1

x = [5 ± √(25 + 16)] / 2

x = [5 ± √41] / 2

So the two solutions for x are:

1. x = (5 + √41) / 2
2. x = (5 - √41) / 2

These are the values of x for which the function y = (5x + 2)/(x^2 - x - 2) is equal to 1.