Rút gọn

To simplify the expressions in the problem, here are the steps for the first equation you've posted:

### Equation 1
\[
\sqrt{x + 4} = \sqrt{7 - 2x} + \sqrt{4 - x}
\]

### Steps to Simplify:

1. **Square Both Sides:**
\[
(\sqrt{x + 4})^2 = \left(\sqrt{7 - 2x} + \sqrt{4 - x}\right)^2
\]
This results in:
\[
x + 4 = (7 - 2x) + 2\sqrt{(7 - 2x)(4 - x)} + (4 - x)
\]
Combine like terms:
\[
x + 4 = 11 - 3x + 2\sqrt{(7 - 2x)(4 - x)}
\]
Thus:
\[
4x - 7 = 2\sqrt{(7 - 2x)(4 - x)}
\]

2. **Square Again:**
\[
(4x - 7)^2 = 4(7 - 2x)(4 - x)
\]
Which results in:
\[
16x^2 - 56x + 49 = 4(28 - 7x - 8x + 2x^2)
\]
Simplifying:
\[
16x^2 - 56x + 49 = 4(28 - 15x + 2x^2)
\]
Thus:
\[
16x^2 - 56x + 49 = 112 - 60x + 8x^2
\]
Rearranging gives:
\[
8x^2 + 4x - 63 = 0
\]

3. **Solve Quadratic Equation:**
Using the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), where \(a = 8, b = 4, c = -63\):
\[
x = \frac{-4 \pm \sqrt{16 + 2016}}{16}
\]
This simplifies to:
\[
x = \frac{-4 \pm 44}{16}
\]
Thus,
\[
x = \frac{40}{16} \text{ or } x = \frac{-48}{16}
\]
This gives:
\[
x = 2.5 \text{ or } x = -3
\]

### Check Validity:
Considering the domain \(x \geq -4\), check \(x = 2.5\) and \(x = -3\) in the original equations.

### Conclusion:
You can simplify the other problems in the same fashion by applying algebraic manipulations, squaring when necessary, and checking for extraneous solutions. If you need help with specific equations, feel free to ask!