n^3−3∗n^2+2∗n=2190

asked by guest
on Oct 18, 2024 at 11:24 pm



You asked:

Solve the equation \({n}^{3} - 3 \cdot {n}^{2} + 2 n = 2190\) for the variable \(n\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}n &= 1 + \sqrt[3]{1095 + \frac{\sqrt{97121022}}{9}} + \frac{1}{3 \sqrt[3]{1095 + \frac{\sqrt{97121022}}{9}}} \approx 14.011847\\n &= - \frac{\sqrt[3]{\frac{\sqrt{97121022}}{9} + 1095}}{2} - \frac{1}{6 \sqrt[3]{\frac{\sqrt{97121022}}{9} + 1095}} + 1 + i \left(- \frac{\sqrt{3}}{6 \sqrt[3]{\frac{\sqrt{97121022}}{9} + 1095}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{97121022}}{9} + 1095}}{2}\right) \approx -5.5059234 + 11.224131 i\\n &= - \frac{\sqrt[3]{\frac{\sqrt{97121022}}{9} + 1095}}{2} - \frac{1}{6 \sqrt[3]{\frac{\sqrt{97121022}}{9} + 1095}} + 1 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{97121022}}{9} + 1095}}{2} + \frac{\sqrt{3}}{6 \sqrt[3]{\frac{\sqrt{97121022}}{9} + 1095}}\right) \approx -5.5059234 -11.224131 i\end{aligned}\]

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

+ Submit Question