Solve simple rational and radical equations and identify extraneous solutions.
Approximate every valid real root with restrictions and tolerance
Problem
For \(\sqrt{x}~+~x~=~10\), state the restrictions, check every candidate in the original equation, and report all valid real roots to the nearest tenth.
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What this problem is really about
Isolate the principal square root and record two restrictions: its radicand must be nonnegative, and the expression on the other side must also be nonnegative. Squaring may produce candidates outside that original interval, so test every one in the unsquared equation. Only after filtering the candidates should you round the complete valid root set to the requested precision.
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