step 1 Okay, so on the left side here we have square root sign and to eliminate it we need to take squa

Solve. √(13-x)=x-1

Name: Problem 15, Chapter 7: Intermediate Algebra
Uploaded: 2020-07-19T01:52:38-08:00
Duration: 2 min 15 s
Channel: Vishal Parmar
Description: Solve. √(13-x)=x-1

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Key Concepts

Squaring Both Sides

Squaring both sides is a common method used to eliminate radicals from an equation. Although this technique simplifies the equation, it can also introduce solutions that do not satisfy the original radical equation, making subsequent verification necessary.

Extraneous Solutions

Extraneous solutions are potential answers that emerge from the process of solving the equation—particularly after operations like squaring—that do not actually satisfy the original equation. Verification of all solutions within the initial equation is crucial to confirm their validity.

Domain Restrictions

Domain restrictions refer to the allowable values of the variable that ensure the expression under the radical is valid (for example, non-negative in the case of square roots). Identifying these restrictions is essential to avoid considering solutions that would result in undefined or invalid expressions within the original equation.

Radical Equations

A radical equation is an equation where the variable appears under a radical (such as a square root). Solving these equations typically requires isolating the radical term and raising both sides of the equation to the appropriate power to remove the radical, keeping in mind the risk of introducing extraneous solutions.

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