Question

(2х-5)⁴+2(2х-5)²-99=0​

Answer 1

Ответ прикреплён. Удачи.

Answer 2

To solve the equation (2x-5)^4 + 2(2x-5)^2 - 99 = 0, you can use a substitution to make it easier to solve. Let's substitute (2x-5)^2 with a new variable, say u:

u = (2x-5)^2

Now, the equation becomes:

u^2 + 2u - 99 = 0

This is a quadratic equation in terms of u, and you can solve it using the quadratic formula:

u = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 1, b = 2, and c = -99. Plugging these values into the quadratic formula:

u = (-2 ± √(2² - 4(1)(-99))) / (2(1))

u = (-2 ± √(4 + 396)) / 2

u = (-2 ± √400) / 2

u = (-2 ± 20) / 2

Now, you have two possible values for u:

1. u = (-2 + 20) / 2 = 18 / 2 = 9
2. u = (-2 - 20) / 2 = -22 / 2 = -11

Now that you have the values of u, you can revert back to the original variable (2x-5)^2:

1. (2x-5)^2 = 9
2. (2x-5)^2 = -11

For the first equation:

Take the square root of both sides:

2x-5 = ±√9 2x-5 = ±3

Now, solve for x in both cases:

1. 2x-5 = 3 2x = 3 + 5 2x = 8 x = 8/2 x = 4

2. 2x-5 = -3 2x = -3 + 5 2x = 2 x = 2/2 x = 1

So, there are two possible solutions for x:

x = 4 and x = 1.

For the second equation (2x-5)^2 = -11, there are no real solutions because the square of a real number cannot be negative. So the only solutions are x = 4 and x = 1.

Answer 3

To solve the equation (2x-5)^4 + 2(2x-5)^2 - 99 = 0, you can use a substitution to simplify it. Let's use a substitution to make the equation easier to work with:

Let u = (2x-5).

Now, substitute u into the equation:

u^4 + 2u^2 - 99 = 0.

Now, this is a quadratic equation in terms of u. To solve it, you can use the quadratic formula:

u = (-b ± √(b^2 - 4ac)) / (2a).

In this case, a = 1, b = 2, and c = -99. Plug these values into the quadratic formula:

u = (-2 ± √(2^2 - 4(1)(-99))) / (2(1)).

Now, calculate the values of u:

u = (-2 ± √(4 + 396)) / 2, u = (-2 ± √400) / 2, u = (-2 ± 20) / 2.

This yields two possible values for u:

1. u = (18) / 2 = 9,
2. u = (-22) / 2 = -11.

Now that you have these values of u, you can substitute them back into the original equation to find the corresponding values of x:

1. For u = 9: 2x - 5 = 9, 2x = 14, x = 7.

2. For u = -11: 2x - 5 = -11, 2x = -6, x = -3.

So, the solutions to the equation (2x-5)^4 + 2(2x-5)^2 - 99 = 0 are x = 7 and x = -3.