Pregunta
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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\( p=16 \)
Solución
Solve the equation \( \sqrt{p-7}+1=4 \).
Solve the equation by following steps:
- step0: Solve for \(p\):
\(\sqrt{p-7}+1=4\)
- step1: Find the domain:
\(\sqrt{p-7}+1=4,p\geq 7\)
- step2: Move the constant to the right side:
\(\sqrt{p-7}=4-1\)
- step3: Subtract the numbers:
\(\sqrt{p-7}=3\)
- step4: Raise both sides to the \(2\)-th power\(:\)
\(\left(\sqrt{p-7}\right)^{2}=3^{2}\)
- step5: Evaluate the power:
\(p-7=9\)
- step6: Move the constant to the right side:
\(p=9+7\)
- step7: Add the numbers:
\(p=16\)
- step8: Check if the solution is in the defined range:
\(p=16,p\geq 7\)
- step9: Find the intersection:
\(p=16\)
- step10: Check the solution:
\(p=16\)
The solution to the equation \( \sqrt{p-7}+1=4 \) is \( p=16 \).
Respondido por UpStudy AI y revisado por un tutor profesional
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Simplifique esta solución The Deep Dive
To solve the equation \( \sqrt{p-7}+1=4 \), we first isolate the square root by subtracting 1 from both sides. This gives us \( \sqrt{p-7} = 3 \). Next, we square both sides to eliminate the square root, leading to \( p - 7 = 9 \). Finally, we solve for \( p \) by adding 7 to both sides, resulting in \( p = 16 \). So, the solution is \( p = 16 \). To check our work, we can substitute \( p = 16 \) back into the original equation: \( \sqrt{16-7}+1 = \sqrt{9}+1 = 3+1 = 4 \), which confirms that our solution is correct!
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