Solve the equations. √(2 a+2)=a+1

Name: Problem 4, Chapter 7: Intermediate Algebra
Uploaded: 2020-06-23T05:33:38-08:00
Duration: 1 min 5 s
Channel: Ankit Gupta
Description: Solve the equations. √(2 a+2)=a+1

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Key Concepts

Extraneous Solutions

Extraneous solutions are the results that emerge from the algebraic process, such as squaring both sides, which may not satisfy the original equation. It is important to check each derived solution within the original equation to confirm its validity.

Domain Restrictions

Radical expressions, particularly square roots, require that the radicand (the expression inside the radical) be nonnegative in the context of real numbers. Assessing and enforcing these domain restrictions is crucial to ensure that all potential solutions are valid.

Squaring Both Sides

Squaring both sides of an equation is a standard technique used to remove a square root from an equation. This step simplifies the equation but must be done with care, as it can potentially introduce solutions that do not satisfy the original equation.

Radical Equations

Radical equations are equations that include a variable within a radical, typically a square root. Solving these equations generally involves isolating the radical expression and then eliminating the radical by raising both sides of the equation to a power that corresponds to the index of the radical.

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