309w^3-3000w=48000

asked by guest
on Nov 29, 2024 at 11:22 am



You asked:

Solve the equation \(309 {w}^{3} - 3000 w = 48000\) for the variable \(w\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}w &= 10 \sqrt[3]{\frac{8}{103} + \frac{2 \sqrt{13672014}}{95481}} + \frac{100}{309 \sqrt[3]{\frac{8}{103} + \frac{2 \sqrt{13672014}}{95481}}} \approx 5.975393\\w &= - 5 \sqrt[3]{\frac{2 \sqrt{13672014}}{95481} + \frac{8}{103}} - \frac{50}{309 \sqrt[3]{\frac{2 \sqrt{13672014}}{95481} + \frac{8}{103}}} + i \left(- \frac{50 \sqrt{3}}{309 \sqrt[3]{\frac{2 \sqrt{13672014}}{95481} + \frac{8}{103}}} + 5 \sqrt{3} \sqrt[3]{\frac{2 \sqrt{13672014}}{95481} + \frac{8}{103}}\right) \approx -2.9876965 + 4.1316163 i\\w &= - 5 \sqrt[3]{\frac{2 \sqrt{13672014}}{95481} + \frac{8}{103}} - \frac{50}{309 \sqrt[3]{\frac{2 \sqrt{13672014}}{95481} + \frac{8}{103}}} + i \left(- 5 \sqrt{3} \sqrt[3]{\frac{2 \sqrt{13672014}}{95481} + \frac{8}{103}} + \frac{50 \sqrt{3}}{309 \sqrt[3]{\frac{2 \sqrt{13672014}}{95481} + \frac{8}{103}}}\right) \approx -2.9876965 -4.1316163 i\end{aligned}\]

\(i\) is the imaginary unit, defined as \(i^2 = -1\).

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