Solve sqrt(x+3) = x - 1.

• A. x = (3 - sqrt(17))/2
• B. x = (3 + sqrt(17))/2
• C. x = 3
• D. x = sqrt(17) - 1

Answer: (B)

This type of problem tests solving an equation with a square root by isolating the root and squaring, while checking for extraneous solutions that can arise after squaring.

The square root is always nonnegative, so the right-hand side must be at least zero: x − 1 ≥ 0, which means x ≥ 1. Next, square both sides: x + 3 = (x − 1)² = x² − 2x + 1. Rearranging gives the quadratic x² − 3x − 2 = 0. Solving yields x = (3 ± √17)/2. The smaller root is about −0.56, which does not satisfy x ≥ 1, so it’s not valid for the original equation. The larger root is (3 + √17)/2, which does satisfy the domain and check out in the original equation. Therefore, the solution is x = (3 + √17)/2.