Question

solve: \\(\sqrt3{x^2 - 8} = 2\\)

• \\(x = -4\\)
• \\(x = 4\\)
• \\(x = -4\\) or \\(x = 4\\)
• no real solution

solve: \\(s = 4 + \sqrt{s + 2}\\)

• \\(s = 2\\)
• \\(s = 7\\)
• \\(s = 2\\) or \\(s = 7\\)
• no real solution

Explanation:

Solve the cube root equation

Using the Cube Root Equations knowledge point

$$
LATEXBLOCK0
$$

Solve the square root equation

Using the Solving Radical Equations knowledge point

$$
LATEXBLOCK1
$$

Check for extraneous solutions

Using the Solving Radical Equations knowledge point

$$
LATEXBLOCK2
$$

Thus, \(s = 7\) is the only real solution.

Answer:

Question 1

• (A) \(x = -4\)
• (B) \(x = 4\)
• (C) \(x = -4 \text{ or } x = 4\) (Correct answer)
• (D) no real solution

Question 2

• (A) \(s = 2\)
• (B) \(s = 7\) (Correct answer)
• (C) \(s = 2 \text{ or } s = 7\)
• (D) no real solution