Solve simple rational and radical equations and identify extraneous solutions.
Solve a radical equation by squaring and checking for extraneous solutions
Problem
Solve \(\sqrt{x~+~1}~=~x~-~1\) and reject any extraneous result.
Big Picture
What this problem is really about
Before squaring, use both original sign conditions: the radicand must be nonnegative, and anything equal to a principal square root must also be nonnegative. Squaring can erase that sign information and create extra algebraic candidates. Solve the resulting polynomial, then test every candidate in the unsquared equation so only values satisfying the original signs remain.
Inside Gozunta
Turn the preview into practice.
More than a preview
Gozunta lets you study this problem—and more than 10,000 others.
Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.
