Question

X³ - x² - 25x + 25 = 0​

Answer 1

Ответ:

Все на фото, удачі)))))))

Answer 2

X^2(x-1)-25(x-1)=0
(X-1)(x^2-25)=0
X-1=0. X^2-25=0
X=1. (X-5)(x+5)=0
X=5 или x= -5

Answer 3

To solve the equation x³ - x² - 25x + 25 = 0, you can use various methods such as factoring, the rational root theorem, or numerical methods. Let's solve it using the rational root theorem and synthetic division.

The rational root theorem states that if a rational number p/q (where p and q are integers) is a root of a polynomial equation with integer coefficients, then p must be a factor of the constant term (in this case, 25), and q must be a factor of the leading coefficient (which is 1).

In this case, the constant term is 25, and the leading coefficient is 1. Therefore, the possible rational roots are the factors of 25 divided by the factors of 1, which simplifies to just the factors of 25. The factors of 25 are ±1, ±5, ±25.

Let's try these possible rational roots by performing synthetic division:

For x = 1:

markdownCopy code
   1 |  1  -1  -25  25
      |    1    0  -25
      |_____________
         1    0   -25   0

Since the remainder is zero, x = 1 is a root.

Now we have factored the equation as (x - 1)(x² - 25) = 0.

Next, let's solve the quadratic equation x² - 25 = 0 by factoring: (x - 1)(x + 5)(x - 5) = 0

Therefore, the solutions to the equation x³ - x² - 25x + 25 = 0 are x = 1, x = -5, and x = 5.