Question

Solve the equation. $$ \sqrt{5 t+4}-2 \sqrt{t}=1 $$

   Solve the equation. 
$$
\sqrt{5 t+4}-2 \sqrt{t}=1
$$

Precalculus

Raymond A. Barnett,… 7th Edition

Chapter 1, Problem 34

Instant Answer

Solved by Expert Brandon Cleary

07/16/2021

Step 1

This gives us: $$ \sqrt{5t+4} = 2\sqrt{t} + 1 $$ Show more…

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Solve the equation. $$ \sqrt{5 t+4}-2 \sqrt{t}=1 $$

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Key Concepts

Radical Equations

Radical equations are equations that contain a variable under a radical, commonly a square root. These types of equations often require special techniques to simplify and solve, such as isolating the radical expression before eliminating the radical.

Domain Considerations

When working with square roots, it is crucial to consider the domain restrictions since the radicand must be non-negative. This ensures that the solutions obtained are valid within the context of the problem.

Isolating the Radical Expression

Isolating the radical involves rearranging the equation so that the radical term is by itself on one side. This step is essential as it prepares the equation for the process of eliminating the radical by raising both sides to a power.

Squaring Both Sides

Squaring both sides of an equation is a common method used to remove square root signs. However, this operation can introduce extraneous solutions that might not be valid in the original equation, so it must be done carefully.

Extraneous Solutions

Extraneous solutions are results that emerge from algebraic manipulations, such as squaring both sides, which do not satisfy the original equation. It is important to check any potential solutions against the original equation to verify their validity.

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