2700w^3-3000w=48000

asked by guest
on Nov 29, 2024 at 11:19 am



You asked:

Solve the equation \(2700 {w}^{3} - 3000 w = 48000\) for the variable \(w\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}w &= 10 \sqrt[3]{\frac{2}{225} + \frac{\sqrt{46626}}{24300}} + \frac{1}{27 \sqrt[3]{\frac{2}{225} + \frac{\sqrt{46626}}{24300}}} \approx 2.7516886\\w &= - 5 \sqrt[3]{\frac{\sqrt{46626}}{24300} + \frac{2}{225}} - \frac{1}{54 \sqrt[3]{\frac{\sqrt{46626}}{24300} + \frac{2}{225}}} + i \left(- \frac{\sqrt{3}}{54 \sqrt[3]{\frac{\sqrt{46626}}{24300} + \frac{2}{225}}} + 5 \sqrt{3} \sqrt[3]{\frac{\sqrt{46626}}{24300} + \frac{2}{225}}\right) \approx -1.3758443 + 2.1372252 i\\w &= - 5 \sqrt[3]{\frac{\sqrt{46626}}{24300} + \frac{2}{225}} - \frac{1}{54 \sqrt[3]{\frac{\sqrt{46626}}{24300} + \frac{2}{225}}} + i \left(- 5 \sqrt{3} \sqrt[3]{\frac{\sqrt{46626}}{24300} + \frac{2}{225}} + \frac{\sqrt{3}}{54 \sqrt[3]{\frac{\sqrt{46626}}{24300} + \frac{2}{225}}}\right) \approx -1.3758443 -2.1372252 i\end{aligned}\]

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

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