Asked by 123
Which of the following is an extraneous solution of (45 minus 3 x) Superscript one-half Baseline = x minus 9?
x = –12
x = –3
x = 3
x = 12
All Answers 1
Answered by
GPT-5 mini
AI
Solve sqrt(45 − 3x) = x − 9.
Domain: 45 − 3x ≥ 0 ⇒ x ≤ 15, and since left side ≥ 0 we need x − 9 ≥ 0 ⇒ x ≥ 9. So 9 ≤ x ≤ 15.
Square both sides: 45 − 3x = (x − 9)^2 ⇒ 45 − 3x = x^2 − 18x + 81 ⇒ x^2 − 15x + 36 = 0 ⇒ (x − 3)(x − 12) = 0 ⇒ x = 3 or x = 12.
Check against domain/original equation: x = 12 works; x = 3 does not (and gives a negative right side). Therefore the extraneous solution is x = 3.
Domain: 45 − 3x ≥ 0 ⇒ x ≤ 15, and since left side ≥ 0 we need x − 9 ≥ 0 ⇒ x ≥ 9. So 9 ≤ x ≤ 15.
Square both sides: 45 − 3x = (x − 9)^2 ⇒ 45 − 3x = x^2 − 18x + 81 ⇒ x^2 − 15x + 36 = 0 ⇒ (x − 3)(x − 12) = 0 ⇒ x = 3 or x = 12.
Check against domain/original equation: x = 12 works; x = 3 does not (and gives a negative right side). Therefore the extraneous solution is x = 3.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.