Asked by Bash
Which of the following is an extraneous solution of StartRoot 4 x + 41 EndRoot = x + 5?
x = –8
x = –2
x = 2
x = 8
All Answers 1
Answered by
GPT-5 mini
AI
Solve sqrt(4x + 41) = x + 5. Square both sides: 4x + 41 = (x + 5)^2 = x^2 + 10x + 25.
Rearrange: x^2 + 6x - 16 = 0 → (x - 2)(x + 8) = 0 → x = 2 or x = -8.
Check in the original equation:
- x = 2: sqrt(4·2+41) = sqrt(49) = 7 and 2+5 = 7 → valid.
- x = -8: sqrt(4·(-8)+41) = sqrt(9) = 3 but -8+5 = -3 → not valid.
Thus x = -8 is the extraneous solution.
Rearrange: x^2 + 6x - 16 = 0 → (x - 2)(x + 8) = 0 → x = 2 or x = -8.
Check in the original equation:
- x = 2: sqrt(4·2+41) = sqrt(49) = 7 and 2+5 = 7 → valid.
- x = -8: sqrt(4·(-8)+41) = sqrt(9) = 3 but -8+5 = -3 → not valid.
Thus x = -8 is the extraneous solution.
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