Pregunta
6:45
5G
Solving Radical Equations
Radical Functions
Solve the equation.
Enter the smallest solution first.
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5G
Solving Radical Equations
Radical Functions
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Ask by May Blake. in the United States
Jan 21,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The solutions are
and
.
Solución

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Respondido por UpStudy AI y revisado por un tutor profesional
Como
Mind Expander
To solve the equation
, first, isolate the square root:
Next, square both sides to eliminate the square root:
Expanding the right side gives:
Rearranging the equation leads to:
Factoring gives:
Thus, the solutions are
and
. The smallest solution is
.
So, the final answer is:
In real-world applications, radical equations can often arise in physics when calculating distances, speeds, or even in engineering when dealing with structural loads. It’s vital to understand how to manipulate these equations, as solving them correctly can lead to practical solutions in various fields.
Also, when solving radical equations, a common mistake is neglecting to check for extraneous solutions. Squaring both sides can introduce solutions that don’t satisfy the original equation. After finding the solutions, always substitute them back into the original equation to ensure they are valid!
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