Question

Solve the radical equation 3x−11−−−−−−√+5=x+2
.(1 point)

x=4


x=−5


x=4
or x=−5


x=4
or x=5

Answer 1

Solve sqrt(3x − 11) + 5 = x + 2.

Rearrange: sqrt(3x − 11) = x − 3. Domain: 3x − 11 ≥ 0 ⇒ x ≥ 11/3, and x − 3 ≥ 0 ⇒ x ≥ 3, so x ≥ 11/3.

Square both sides: 3x − 11 = (x − 3)^2 = x^2 − 6x + 9 → x^2 − 9x + 20 = 0 → (x − 4)(x − 5) = 0.

Thus x = 4 or x = 5. Both satisfy the original equation, so the solution is x = 4 or x = 5.