Question

7. Solve the radical equation9−2x+4−−−−−−−−√=x+1 Which of the following are the correct solutions?(1 point)x=2 x=3 x=2 or x=3 No real solution

Answer 1

Interpret the equation as sqrt(13 − 2x) = x + 1.

Domain: x + 1 ≥ 0 ⇒ x ≥ −1.

Square both sides:
13 − 2x = (x + 1)^2 = x^2 + 2x + 1
0 = x^2 + 4x − 12 = (x − 2)(x + 6)

So x = 2 or x = −6. Only x = 2 satisfies the domain (x ≥ −1). Check: sqrt(13 − 4) = 3 = 2 + 1.

Correct choice: x = 2.