Find all real solutions to each equation. Check your answers. √(x^2-2 x-15)=3

Name: Problem 19, Chapter 3: Precalculus Functions and Graphs
Uploaded: 2020-04-17T01:52:45-08:00
Duration: 3 min 27 s
Channel: Shamshad Waris
Description: Find all real solutions to each equation. Check your answers. √(x^2-2 x-15)=3

step 1 We have a given an equation root under x squared minus 2 x minus 15 is called to 0. Sorry 3. Now

Find all real solutions to each equation. Check your...

Key Concepts

Radical Equations

Radical equations are equations in which the variable appears under a radical sign, such as a square root. To solve these equations properly, it is necessary to consider the domain restrictions imposed by the radical (usually requiring the expression under the radical to be non-negative) and proceed with algebraic manipulations like squaring both sides, keeping in mind this operation might introduce extraneous solutions.

Domain Restrictions

When working with square root functions, the expression inside the square root (the radicand) must be non-negative in order for the function to be defined in the real number system. This condition is used to restrict the possible solutions before further manipulation of the equation.

Squaring Both Sides

Squaring both sides of an equation is a common strategy for eliminating square roots, which can simplify the equation and make it more straightforward to solve. However, squaring is not a reversible operation in all cases, which means extraneous solutions can be introduced. Consequently, any solutions obtained after squaring must be checked against the original equation.

Extraneous Solutions

Extraneous solutions are results derived from algebraic manipulations (such as squaring both sides) that do not satisfy the original equation. To avoid incorrectly accepting these solutions, it is important to substitute all potential solutions back into the original equation and verify that they work within its initial constraints.

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