知识点 6
Solve equations involving radicals; check for extraneous solutions.
Isolate the radical, square carefully, and check for extraneous solutions.
核心知识
Isolate the radical before squaring, and always check the result in the original equation because squaring can create an answer that was never valid.
深入理解
Rule: Radical equations feel routine until the final check. Once you square both sides, you may have introduced a false solution.
On ACT, the right workflow is short: isolate the radical, square carefully, solve the resulting equation, then substitute each candidate back into the original radical equation. Do not skip that last step.
分步讲解
- Isolate the radical.
- Square both sides and solve the resulting equation.
- Check every candidate in the original equation.
常见误解
- Assuming every solution from the squared equation is valid.
- Squaring before isolating the radical.
- Skipping the final check.
题目
示例解析
What is the solution to
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