Question

Решите уравнение : Корень из 2x+6= 1-x Пожалуйста помогите!!!!!

Answer 1

ОДЗ

2x+6>=0

x>=-3

1-x>=0

x<=1

2x+6=1-2x+x^2

x^2-2x+1-2x-6=0

x^2-4x-5=0

D=16+20=36

x1=(4+6)/2=10/2=5 не удовл

x2=(4-6)/2=-2/2=-1

Answer 2

Solving the Equation: $\sqrt{2x+6} = 1-x$

To solve the equation $\sqrt{2x+6} = 1-x$, we can follow these steps:

1. Isolate the Radical Term: - First, isolate the radical term on one side of the equation.

2. Square Both Sides: - Then, square both sides of the equation to eliminate the square root.

3. Solve for x: - After squaring both sides, solve for the variable x.

Step-by-Step Solution:

1. Isolate the Radical Term: - The given equation is $\sqrt{2x+6} = 1-x$.

2. Square Both Sides: - Squaring both sides of the equation gives us $2x+6 = (1-x)^2$.

3. Solve for x: - Expanding the right-hand side gives us $2x+6 = 1-2x+x^2$. - Rearranging the terms gives us the quadratic equation $x^2+3x-5=0$.

4. Use the Quadratic Formula: - We can use the quadratic formula $x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$ to solve for x, where a=1, b=3, and c=-5.

5. Calculate the Solutions: - Plugging the values into the quadratic formula gives us the solutions: $x = \frac{-3 \pm \sqrt{3^2-4*1*(-5)}}{2*1}$. - Simplifying further gives us the solutions: $x = \frac{-3 \pm \sqrt{29}}{2}$.

So, the solutions to the equation $\sqrt{2x+6} = 1-x$ are: - $x = \frac{-3 + \sqrt{29}}{2}$ - $x = \frac{-3 - \sqrt{29}}{2}$

I hope this helps! If you have any further questions, feel free to ask.