Pregunta
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Respuesta verificada por el tutor
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\( x = -6 \)
Solución
Solve the equation \( x^{3}+216=0 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(x^{3}+216=0\)
- step1: Move the constant to the right side:
\(x^{3}=0-216\)
- step2: Remove 0:
\(x^{3}=-216\)
- step3: Simplify the equation:
\(\sqrt[3]{x^{3}}=\sqrt[3]{-216}\)
- step4: Calculate:
\(x=\sqrt[3]{-216}\)
- step5: Simplify the root:
\(x=-6\)
The solution to the equation \(x^{3}+216=0\) is \(x=-6\).
Respondido por UpStudy AI y revisado por un tutor profesional
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Simplifique esta solución The Deep Dive
To solve the equation \( x^{3}+216=0 \), we can first rewrite it as \( x^{3} = -216 \). Recognizing that \( -216 \) is the same as \( -6^3 \), we can see that one solution is \( x = -6 \). However, there are actually three possible solutions to this equation because it is a cubic equation. The other two solutions can be found using the roots of unity. We can express \( -216 \) in polar form and find the complex roots. The full set of solutions includes \( x = -6 \), \( x = 3 + 3i\sqrt{3} \), and \( x = 3 - 3i\sqrt{3} \).
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