Question

Корень 4+2x-x^2=x-2 Помогите позязя

Answer 1

Вот а проверку сама сделаешь

Answer 2

4 + 2x - x² = x - 2
4 + 2x - x² - x + 2 = 0
- x² + x + 6 = 0
x² - x - 6 = 0
x₁ + x₂ = 1
x₁ * x₂ = - 6
x₁ = 3; x₂ = - 2

Ответ: - 2; 3

Answer 3

I can help you solve this equation step by step. The equation is:

$$\sqrt{4+2x-x^2}=x-2$$

First, we need to square both sides of the equation to get rid of the square root. This gives us:

$$4+2x-x^2=(x-2)^2$$

Next, we need to expand the right side and simplify the equation. This gives us:

$$-2x^2+6x=0$$

Now, we can factor out a common factor of -2x from both terms. This gives us:

$$-2x(x-3)=0$$

Finally, we can use the zero product property to find the values of x that make the equation true. This gives us:

$$x=0 \text{ or } x=3$$

However, we need to check if these solutions are valid, because squaring both sides of the equation might introduce extraneous solutions. To do this, we need to plug in the values of x into the original equation and see if they satisfy it. This gives us:

$$\sqrt{4+2(0)-(0)^2}=0-2 \implies 2=-2 \text{ (false)}$$

$$\sqrt{4+2(3)-(3)^2}=3-2 \implies 1=1 \text{ (true)}$$

Therefore, the only valid solution is x=3. You can see the graph of the equation and the solution here.

I hope this helps you understand how to solve this equation. If you have any other questions, feel free to ask me.