Advanced MathHardRadical equation with an extraneous root
Advanced Math practice question
What is the solution to the equation √(2x + 7) = x + 2?
Answer: 1
Squaring gives 2x + 7 = x² + 4x + 4, so x² + 2x − 3 = 0 and x = 1 or x = −3. Only x = 1 checks: √9 = 3. At x = −3, √1 = 1 but x + 2 = −1.
Common wrong answers
- If you answered 3
- 3 gives √13 on the left and 5 on the right.
- If you answered -3
- −3 is the extraneous root; the right side would be −1.
- If you answered -1
- −1 gives √5 on the left and 1 on the right.
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