Question

√(9-x^2) = -|x^2+4x+3|

Answer 1

3-x=x^2+4x+3
3-x-x^2-4x-3=0
-x^2-5x=0 /-1
x^2+5x=0
x(x+5)=0
1.x=0
2.x+5=0
x=-5
по-моему так будет

Answer 2

Let's solve the equation step by step.

First, let's focus on the right-hand side of the equation:

|-|x^2 + 4x + 3||

The expression inside the absolute value signs can be negative or positive, so we need to consider both cases.

Case 1: x^2 + 4x + 3 is positive In this case, the absolute value becomes:

|x^2 + 4x + 3| = x^2 + 4x + 3

Case 2: x^2 + 4x + 3 is negative In this case, the absolute value becomes:

|x^2 + 4x + 3| = -(x^2 + 4x + 3) = -x^2 - 4x - 3

Now, let's substitute these values back into the original equation:

√(9 - x^2) = -|x^2 + 4x + 3|

Case 1: x^2 + 4x + 3 is positive √(9 - x^2) = -(x^2 + 4x + 3)

Squaring both sides of the equation to eliminate the square root:

9 - x^2 = (x^2 + 4x + 3)^2 9 - x^2 = x^4 + 8x^3 + 25x^2 + 24x + 9

Rearranging the equation and combining like terms:

0 = x^4 + 8x^3 + 25x^2 + 24x 0 = x(x^3 + 8x^2 + 25x + 24)

At this point, we have two possibilities:

1. x = 0
2. x^3 + 8x^2 + 25x + 24 = 0

Case 2: x^2 + 4x + 3 is negative √(9 - x^2) = x^2 + 4x + 3

Squaring both sides of the equation:

9 - x^2 = (x^2 + 4x + 3)^2 9 - x^2 = x^4 + 8x^3 + 25x^2 + 24x + 9

Rearranging the equation and combining like terms:

0 = x^4 + 8x^3 + 25x^2 + 24x 0 = x(x^3 + 8x^2 + 25x + 24)

At this point, we have two possibilities:

1. x = 0
2. x^3 + 8x^2 + 25x + 24 = 0

Now, we need to solve the cubic equation x^3 + 8x^2 + 25x + 24 = 0. This can be done using numerical methods or factoring techniques.

Unfortunately, the solutions to the cubic equation are quite complex, involving irrational numbers and radicals. It is not possible to find exact solutions without numerical approximations.

In summary, the solutions to the equation √(9 - x^2) = -|x^2 + 4x + 3| involve the solutions to the cubic equation x^3 + 8x^2 + 25x + 24 = 0, as well as the possibility of x = 0.