Question

√(2x+9)^2*√3=√192или √(2x+9)^2=8

Answer 1

√(2x+9)^2*√3=√192   или √(2x+9)^2=8

Оба уравнения абсолютно одинаковы, просто первое упростили до второго следующим образом

$\sqrt{(2x+9) ^{2}}* \sqrt{3} = \sqrt{192} \\ \sqrt{(2x+9) ^{2}} = \frac{ \sqrt{192} }{ \sqrt{3} } \\ \sqrt{(2x+9) ^{2}} = \sqrt{ \frac{192}{3} } \\ \sqrt{(2x+9) ^{2}} = \sqrt{64} \\ \sqrt{(2x+9) ^{2}} = 8$
|2x + 9| = 8
2x + 9 = 8            или          2x + 9 = -8
2x = -1                                 2x = -17
x = $-\frac{1}{2}$                                x = $-\frac{17}{2}$
Ответ:      $x = -\frac{1}{2}$                           $x = -8\frac{1}{2}$                                      

Answer 2

2x+9=8 или 2x+9=-8
Из первого уравнения x1=-0,5
Из второго уравнения x2=-8,5

Answer 3

Let's solve the equation step by step:

1. √(2x+9)^2 * √3 = √192

To simplify this, we can first simplify the expressions inside the square roots:

√(2x+9)^2 = |2x+9|, because the square root of a square cancels out the square.

Now the equation becomes:

|2x + 9| * √3 = √192

2. √(2x+9)^2 = 8

Similarly, we can simplify this expression inside the square root:

√(2x+9)^2 = |2x+9|

Now the equation becomes:

|2x + 9| = 8

Now, we have two separate equations to solve:

1. |2x + 9| * √3 = √192
2. |2x + 9| = 8

Let's solve each equation:

1. |2x + 9| * √3 = √192

Divide both sides by √3:

|2x + 9| = √192 / √3

Since √(192/3) = √(64) = 8, the equation becomes:

|2x + 9| = 8

This equation is the same as the one in equation 2.

Therefore, both equations are equivalent, and we have:

|2x + 9| = 8

Now, to solve for x, we'll consider two cases:

Case 1: 2x + 9 = 8

Subtract 9 from both sides:

2x = -1

Divide both sides by 2:

x = -1/2

Case 2: -(2x + 9) = 8

Distribute the negative sign:

-2x - 9 = 8

Add 9 to both sides:

-2x = 17

Divide both sides by -2:

x = -17/2

So, the two possible solutions for x are x = -1/2 and x = -17/2.