Radical Equations Algebra 2 Flashcards

Solving Radical Equations

• Solutions to radical equations must be verified for extraneous roots which can appear during the solving process.
• Various forms of solutions include single values, positives and negatives, or multiple disallowed values.

Specific Solutions

• x = 32: A straightforward radical equation with no extraneous solutions.
• x = ±125: Indicates two possible solutions; check for extraneous values.
• x = 20 (x ≠ 5) and x = 5 (x ≠ -2): Requires verification to exclude invalid results.
• x = 67, x = 44, x = 1 or 3, x = 4, x = 8, x = 3 (x ≠ -2), x = 12: All solutions require extraneous checks.
• x = -1, x = 49, x = -8: Solutions obtained from solving simple radical equations, some needing verification for extraneous results.
• x = 27: Result from the equation √(2x - 5) = 7.
• x = 16: Obtained from solving √(x - 7) = 3.
• x = 225: Derived from -10 + √x = 5.
• x = 5: Found through the equation 4√(2x - 1) = 12.
• x = 2: Result from √(x - 1) = √(3x - 5).
• x = 24: Solution to 5 = √(x + 1).
• x = -2: From the equation 2 = √(-2x).
• x = 11, x = 54, x = 11/3, x = 25: Each of these results comes from different radical equations requiring careful investigation of all potential solutions.

Critical Concepts

• Solutions may appear valid but must be tested against the criteria of the original equation.
• Disallowed values (e.g., x ≠ -2) indicate restrictions based on radical equations, preventing certain solutions from being legitimate.
• Certain problems involve cube roots (e.g., x = 25 from ∛(2x + 14) = 4) which expands the type of radical equations encountered.

General Strategy

• Isolate the radical expression before squaring both sides to eliminate the root.
• Retain attention on the potential for extraneous solutions that could arise from the squaring process.
• Always simplify and communicate solutions clearly, addressing any restrictions explicitly.