√(3-3 p)-3=√(3 p+2)

Name: Problem 47, Chapter 7: Algebra for College Students
Uploaded: 2022-02-25T18:30:53-08:00
Duration: 6 min 15 s
Channel: Vivek Kumar
Description: √(3-3 p)-3=√(3 p+2)

Key Concepts

Squaring Both Sides

Squaring both sides of an equation is a common technique used to eliminate square roots and simplify radical equations. While it effectively removes the radicals, this step can introduce extraneous solutions. Thus, caution and subsequent verification of all potential solutions are necessary to ensure they are valid in the original context.

Radical Equations

This concept involves equations that contain radical expressions, particularly square roots. Solving these equations often requires isolating the radical on one side of the equation, followed by operations that remove the radical—commonly squaring both sides—while being mindful of potentially introducing invalid solutions.

Domain Restrictions

Expressions under a square root (or any radical with an even index) must be non-negative for the expression to be defined in the set of real numbers. Thus, establishing the domain restrictions is crucial when solving radical equations to ensure that the solutions lie within the permissible range of values.

Extraneous Solutions

Extraneous solutions are results that arise from the process of solving radical equations, particularly when both sides of an equation are squared. These solutions might satisfy the squared equation but not the original equation. Therefore, it is essential to verify each potential solution by substituting it back into the original equation.

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