solve 9x^4 -355x^2 + 3517.48 = 0

asked by guest
on Jan 24, 2025 at 1:59 am



You asked:

Solve the equation \(9 {x}^{4} - 355 {x}^{2} + 3517.48 = 0\) for the variable \(x\).

MathBot Answer:

The 4 solutions to the equation are: \[\begin{aligned}x &= - \frac{\sqrt{15} \cdot \sqrt[4]{87937} \cos{\left(\frac{\arctan{\left(\frac{\sqrt{15107}}{1775} \right)}}{2} \right)}}{15} - \frac{\sqrt{15} \cdot \sqrt[4]{87937} i \sin{\left(\frac{\arctan{\left(\frac{\sqrt{15107}}{1775} \right)}}{2} \right)}}{15} \approx -4.4436286 -0.15366638 i\\x &= - \frac{\sqrt{15} \cdot \sqrt[4]{87937} \cos{\left(\frac{\arctan{\left(\frac{\sqrt{15107}}{1775} \right)}}{2} \right)}}{15} + \frac{\sqrt{15} \cdot \sqrt[4]{87937} i \sin{\left(\frac{\arctan{\left(\frac{\sqrt{15107}}{1775} \right)}}{2} \right)}}{15} \approx -4.4436286 + 0.15366638 i\\x &= \frac{\sqrt{15} \cdot \sqrt[4]{87937} \cos{\left(\frac{\arctan{\left(\frac{\sqrt{15107}}{1775} \right)}}{2} \right)}}{15} - \frac{\sqrt{15} \cdot \sqrt[4]{87937} i \sin{\left(\frac{\arctan{\left(\frac{\sqrt{15107}}{1775} \right)}}{2} \right)}}{15} \approx 4.4436286 -0.15366638 i\\x &= \frac{\sqrt{15} \cdot \sqrt[4]{87937} \cos{\left(\frac{\arctan{\left(\frac{\sqrt{15107}}{1775} \right)}}{2} \right)}}{15} + \frac{\sqrt{15} \cdot \sqrt[4]{87937} i \sin{\left(\frac{\arctan{\left(\frac{\sqrt{15107}}{1775} \right)}}{2} \right)}}{15} \approx 4.4436286 + 0.15366638 i\end{aligned}\]

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

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