Solve each equation. Check the solutions. p-2 √(p)=8 |...

Name: Problem 46, Chapter 11: Beginning and Intermediate Algebra
Uploaded: 2022-02-15T23:22:10-08:00
Duration: 2 min 27 s
Channel: Victor Salazar
Description: Solve each equation. Check the solutions. p-2 √(p)=8

Key Concepts

Radical Equations

Radical equations are equations that involve a variable inside a radical, typically a square root. A common strategy for solving these equations is to first isolate the radical on one side of the equation, so that you can eliminate the square root by raising both sides of the equation to an appropriate power (usually squaring). This transforms the equation into a form that is often easier to solve, such as a polynomial equation.

Isolating the Radical

Isolating the radical involves rearranging the equation so that the term containing the radical stands by itself on one side. This is an essential step in solving radical equations, as it facilitates the process of squaring both sides of the equation to remove the radical. Without isolating the radical, squaring might lead to a more complicated equation or mix radical and non-radical terms unnecessarily.

Squaring Both Sides

Squaring both sides of an equation is a method used to eliminate square roots by taking advantage of the property that the square of a square root returns the original value under the radical. However, this process must be performed with care, because it can introduce new solutions that do not satisfy the original equation, known as extraneous solutions.

Extraneous Solutions

Extraneous solutions are additional answers that arise from the process of squaring both sides of an equation, but these solutions do not satisfy the original equation. After solving the squared equation, it is imperative to check all potential solutions in the original equation to ensure that they are valid. This step is crucial because operations such as squaring can mask restrictions inherent in the original problem.

Domain Restrictions

Domain restrictions are conditions that limit the set of possible solutions for an equation, particularly when the equation involves a square root. Since the square root function returns only non-negative values when dealing with real numbers, the expression inside the square root must be non-negative. Recognizing these restrictions early on helps avoid considering impossible or non-real solutions during the problem-solving process.

Transcript

Please give Ace some feedback