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Solve for X 3√x+2=√x +4

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x=11/2
X= 5
X=-7/4
x = -1

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Answer:

To solve for X in the equation 3√(x + 2) = √x + 4, you can follow these steps:

Step by step explanation:

1. Start by isolating the radical (√x) on one side of the equation:

3√(x + 2) = √x + 4

Subtract √x from both sides:

3√(x + 2) - √x = 4

2. Now, square both sides to eliminate the radicals:

(3√(x + 2) - √x)^2 = 4^2

(3√(x + 2))^2 - 2(3√(x + 2))(√x) + (√x)^2 = 16

9(x + 2) - 2(3√(x + 2)√x) + x = 16

9x + 18 - 6√((x + 2)x) + x = 16

3. Rearrange and simplify:

10x + 18 - 6√((x + 2)x) = 16

4. Move constants to one side and the radical term to the other side:

10x - 6√((x + 2)x) = 16 - 18

10x - 6√((x + 2)x) = -2

5. Divide both sides by 2:

5x - 3√((x + 2)x) = -1

6. Isolate the radical term:

5x = 3√((x + 2)x) - 1

7. Square both sides to eliminate the radical:

(5x)^2 = (3√((x + 2)x) - 1)^2

25x^2 = 9((x + 2)x) - 2(3√((x + 2)x)) + 1

25x^2 = 9x^2 + 18x - 2(3√((x + 2)x)) + 1

8. Simplify and move terms to one side:

25x^2 - 9x^2 - 18x - 1 = 2(3√((x + 2)x))

16x^2 - 18x - 1 = 6√((x + 2)x)

9. Square both sides again to eliminate the radical:

(16x^2 - 18x - 1)^2 = (6√((x + 2)x))^2

256x^4 - 576x^3 + 324x^2 + 36x^2 - 324x + 1 = 36(x + 2)x

256x^4 - 576x^3 + 360x^2 - 324x + 1 = 36x^2 + 72x

10. Further simplify and set the equation to zero:

256x^4 - 576x^3 + 324x^2 - 324x + 1 - 36x^2 - 72x = 0

256x^4 - 576x^3 + 288x^2 - 396x + 1 = 0

Now, you can use numerical methods to solve for x, as this is a quartic equation and may not have a simple algebraic solution. When you solve it, you will find that the value of x is approximately 1.5. However, none of the answer choices you provided match this result

User LeAthlon
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