7
QuizMultiple Choice

Solving Equations Containing Two Radicals — Quiz

Question 7 • Algebra II

Two possible solutions of square root of 11 minus 2 x end root is equal to square root of x squared plus 4 x plus 4 end root are negative 7 and 1 Which statement is true?

Answer
A
Only x is equal to negative 7 is an extraneous solution.
B
Only x is equal to 1 is an extraneous solution.
C
Both solutions are extraneous.
D
Neither solution is extraneous.

Explanation

Check each candidate in the original equation, √(11 − 2x) = √(x² + 4x + 4). For x = −7, both sides equal √25 = 5. For x = 1, both sides equal √9 = 3. Both candidates satisfy the equation, so neither solution is extraneous; the true statement is “Neither solution is extraneous.”

AI-written and checked against the verified answer.

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