1y^3-1.769y^2-0.298=0

asked by guest
on Jan 25, 2025 at 1:47 am



You asked:

Solve the equation \(1 {y}^{3} - 1.769 {y}^{2} - 0.298 = 0\) for the variable \(y\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}y &= \frac{1769}{3000} + \sqrt[3]{\frac{9558839609}{27000000000} + \frac{\sqrt{6747321610446}}{9000000}} + \frac{3129361}{9000000 \sqrt[3]{\frac{9558839609}{27000000000} + \frac{\sqrt{6747321610446}}{9000000}}} \approx 1.8555507\\y &= - \frac{\sqrt[3]{\frac{\sqrt{6747321610446}}{9000000} + \frac{9558839609}{27000000000}}}{2} - \frac{3129361}{18000000 \sqrt[3]{\frac{\sqrt{6747321610446}}{9000000} + \frac{9558839609}{27000000000}}} + \frac{1769}{3000} + i \left(- \frac{3129361 \sqrt{3}}{18000000 \sqrt[3]{\frac{\sqrt{6747321610446}}{9000000} + \frac{9558839609}{27000000000}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{6747321610446}}{9000000} + \frac{9558839609}{27000000000}}}{2}\right) \approx -0.043275353 + 0.3984049 i\\y &= - \frac{\sqrt[3]{\frac{\sqrt{6747321610446}}{9000000} + \frac{9558839609}{27000000000}}}{2} - \frac{3129361}{18000000 \sqrt[3]{\frac{\sqrt{6747321610446}}{9000000} + \frac{9558839609}{27000000000}}} + \frac{1769}{3000} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{6747321610446}}{9000000} + \frac{9558839609}{27000000000}}}{2} + \frac{3129361 \sqrt{3}}{18000000 \sqrt[3]{\frac{\sqrt{6747321610446}}{9000000} + \frac{9558839609}{27000000000}}}\right) \approx -0.043275353 -0.3984049 i\end{aligned}\]

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

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