Question

1/(x-3)^2-3/x-3-4=0 срочно решите пожалуйста ))

Answer 1

Х-3= не равно 0 х не равен 3
приведем к общему знаменателю(это х-3 в квадрате)
имеем
1-3(х-3)-4(х-3)^2=0
1-3x+9-4(x^2-6x+9)=0
1-3x+9-4x^2+24x-36=0
-4x^2+21x-26=0
дискримимнант = 441-4*(-26)*(-4)=25
х1=(-21+5)/-8=2
x2=(-21-5)/-8=3.25

Answer 2

Solving the Equation

To solve the equation 1/(x-3)^2 - 3/(x-3) - 4 = 0, we can follow these steps:

1. Substitute a Variable: Let's substitute a variable to simplify the equation.

2. Simplify the Equation: After substitution, we can simplify the equation to make it easier to solve.

3. Solve for the Variable: With the simplified equation, we can solve for the variable to find its value.

Step 1: Substituting a Variable

Let's substitute a variable to simplify the equation. We can let y = 1/(x-3).

Step 2: Simplifying the Equation

Substituting y = 1/(x-3), the equation becomes: y^2 - 3y - 4 = 0.

Step 3: Solving for the Variable

Now, we can solve the quadratic equation y^2 - 3y - 4 = 0 to find the values of y.

Using the quadratic formula: y = (-b ± √(b^2 - 4ac)) / (2a), where a = 1, b = -3, and c = -4, we get: y = (3 ± √(9 + 16)) / 2 = (3 ± √25) / 2 = (3 ± 5) / 2.

So, the solutions for y are: y1 = (3 + 5) / 2 = 8 / 2 = 4, y2 = (3 - 5) / 2 = -2 / 2 = -1.

Finding the Values of x

Now that we have the values of y, we can substitute back to find the values of x: For y = 4, 1/(x-3) = 4, For y = -1, 1/(x-3) = -1.

Solving these equations will give us the values of x.

This is the detailed process to solve the given equation. Let me know if you need further assistance!