268329x times 827492x

x=982943

asked by guest
on Jan 20, 2025 at 7:51 am



You asked:

Solve the equation \(268329 x \cdot 827492 x \cdot x = 982943\) for the variable \(x\).

MathBot Answer:

The solutions are given by the formula: \[x = \frac{\sqrt[3]{6057608185227271128424705854} \cos{\left(\frac{2 \pi k}{3} \right)}}{111020050434} + \frac{\sqrt[3]{6057608185227271128424705854} \sin{\left(\frac{2 \pi k}{3} \right)}}{111020050434} i\] where \(k\) is an integer in \(0 \le k < 3\).

There is \(1\) real solution.

There are \(2\) solutions with nonzero imaginary part.

Real solutions: \[\begin{aligned}x &= \frac{\sqrt[3]{6057608185227271128424705854}}{111020050434} \\&\approx 0.016419716\end{aligned}\]

Solutions with nonzero imaginary part: \[\begin{aligned}x &= - \frac{\sqrt[3]{6057608185227271128424705854}}{222040100868} + \frac{\sqrt[3]{2019202728409090376141568618} \cdot 3^{\frac{5}{6}} i}{222040100868} \\&\approx -0.008209858 + 0.014219891 i\\x &= - \frac{\sqrt[3]{6057608185227271128424705854}}{222040100868} - \frac{\sqrt[3]{2019202728409090376141568618} \cdot 3^{\frac{5}{6}} i}{222040100868} \\&\approx -0.008209858 -0.014219891 i\end{aligned}\]

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

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