1y^3-1.805y^2-0.298=0

asked by guest
on Jan 25, 2025 at 1:55 am



You asked:

Solve the equation \(1 {y}^{3} - 1.805 {y}^{2} - 0.298 = 0\) for the variable \(y\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}y &= \frac{361}{600} + \sqrt[3]{\frac{79229881}{216000000} + \frac{\sqrt{282226328070}}{1800000}} + \frac{130321}{360000 \sqrt[3]{\frac{79229881}{216000000} + \frac{\sqrt{282226328070}}{1800000}}} \approx 1.8885523\\y &= - \frac{\sqrt[3]{\frac{\sqrt{282226328070}}{1800000} + \frac{79229881}{216000000}}}{2} - \frac{130321}{720000 \sqrt[3]{\frac{\sqrt{282226328070}}{1800000} + \frac{79229881}{216000000}}} + \frac{361}{600} + i \left(- \frac{130321 \sqrt{3}}{720000 \sqrt[3]{\frac{\sqrt{282226328070}}{1800000} + \frac{79229881}{216000000}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{282226328070}}{1800000} + \frac{79229881}{216000000}}}{2}\right) \approx -0.041776134 + 0.39502858 i\\y &= - \frac{\sqrt[3]{\frac{\sqrt{282226328070}}{1800000} + \frac{79229881}{216000000}}}{2} - \frac{130321}{720000 \sqrt[3]{\frac{\sqrt{282226328070}}{1800000} + \frac{79229881}{216000000}}} + \frac{361}{600} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{282226328070}}{1800000} + \frac{79229881}{216000000}}}{2} + \frac{130321 \sqrt{3}}{720000 \sqrt[3]{\frac{\sqrt{282226328070}}{1800000} + \frac{79229881}{216000000}}}\right) \approx -0.041776134 -0.39502858 i\end{aligned}\]

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

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