solve 9x^4 -355.86x^2 + 3529.35 = 0

asked by guest
on Jan 24, 2025 at 2:02 am



You asked:

Solve the equation \(9 {x}^{4} - 355.86 {x}^{2} + 3529.35 = 0\) for the variable \(x\).

MathBot Answer:

The 4 solutions to the equation are: \[\begin{aligned}x &= - \frac{\sqrt{2} \cdot 5^{\frac{3}{4}} \cdot \sqrt[4]{7843} \cos{\left(\frac{\arctan{\left(\frac{\sqrt{12971}}{1977} \right)}}{2} \right)}}{10} - \frac{\sqrt{2} \cdot 5^{\frac{3}{4}} \cdot \sqrt[4]{7843} i \sin{\left(\frac{\arctan{\left(\frac{\sqrt{12971}}{1977} \right)}}{2} \right)}}{10} \approx -4.4481894 -0.12801872 i\\x &= - \frac{\sqrt{2} \cdot 5^{\frac{3}{4}} \cdot \sqrt[4]{7843} \cos{\left(\frac{\arctan{\left(\frac{\sqrt{12971}}{1977} \right)}}{2} \right)}}{10} + \frac{\sqrt{2} \cdot 5^{\frac{3}{4}} \cdot \sqrt[4]{7843} i \sin{\left(\frac{\arctan{\left(\frac{\sqrt{12971}}{1977} \right)}}{2} \right)}}{10} \approx -4.4481894 + 0.12801872 i\\x &= \frac{\sqrt{2} \cdot 5^{\frac{3}{4}} \cdot \sqrt[4]{7843} \cos{\left(\frac{\arctan{\left(\frac{\sqrt{12971}}{1977} \right)}}{2} \right)}}{10} - \frac{\sqrt{2} \cdot 5^{\frac{3}{4}} \cdot \sqrt[4]{7843} i \sin{\left(\frac{\arctan{\left(\frac{\sqrt{12971}}{1977} \right)}}{2} \right)}}{10} \approx 4.4481894 -0.12801872 i\\x &= \frac{\sqrt{2} \cdot 5^{\frac{3}{4}} \cdot \sqrt[4]{7843} \cos{\left(\frac{\arctan{\left(\frac{\sqrt{12971}}{1977} \right)}}{2} \right)}}{10} + \frac{\sqrt{2} \cdot 5^{\frac{3}{4}} \cdot \sqrt[4]{7843} i \sin{\left(\frac{\arctan{\left(\frac{\sqrt{12971}}{1977} \right)}}{2} \right)}}{10} \approx 4.4481894 + 0.12801872 i\end{aligned}\]

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

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