√(x+5)+√(x+3)=√(2 x+7)

Name: Problem 59, Chapter 7: Mathematics for IIT JEE Main and Advanced Differential Calculus Algebra Trigonometry
Uploaded: 2022-01-02T07:17:22-08:00
Duration: 1 min 27 s
Channel: Aman Gupta
Description: √(x+5)+√(x+3)=√(2 x+7)

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Key Concepts

Radical Equations

Radical equations are equations in which the variable appears under a radical, most commonly a square root. They require special techniques and caution during the process of solving due to the involvement of roots, which have domain constraints and can lead to extraneous solutions when manipulated.

Domain Restrictions

Domain restrictions refer to the necessary conditions that the expressions inside the radicals must satisfy to be defined, typically being non-negative in the case of square roots. Recognizing these restrictions early in the problem-solving process helps to limit the set of potential solutions and avoid invalid results.

Squaring Both Sides

Squaring both sides is a common method used to eliminate square roots in radical equations. By raising both sides of the equation to the power of two, the radicals are removed, thereby transforming the equation into a simpler, often polynomial form. However, this process can introduce solutions that do not satisfy the original equation.

Extraneous Solutions

Extraneous solutions are false solutions that may appear as a result of algebraic manipulations such as squaring both sides of an equation. These solutions do not satisfy the original equation, so it is crucial to check all obtained solutions in the original radical equation to ensure their validity.

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