x(x-4)=(x-2)^3

asked by guest
on Sep 22, 2024 at 10:23 am



You asked:

Solve the equation \(x\left( x - 4 \right) = {\left( x - 2 \right)}^{3}\) for the variable \(x\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}x &= \frac{7}{3} - \frac{1}{3 \sqrt[3]{53 + 6 \sqrt{78}}} - \frac{\sqrt[3]{53 + 6 \sqrt{78}}}{3} \approx 0.68540379\\x &= \frac{1}{6 \sqrt[3]{6 \sqrt{78} + 53}} + \frac{\sqrt[3]{6 \sqrt{78} + 53}}{6} + \frac{7}{3} + i \left(- \frac{\sqrt{3}}{6 \sqrt[3]{6 \sqrt{78} + 53}} + \frac{\sqrt{3} \sqrt[3]{6 \sqrt{78} + 53}}{6}\right) \approx 3.1572981 + 1.3051515 i\\x &= \frac{1}{6 \sqrt[3]{6 \sqrt{78} + 53}} + \frac{\sqrt[3]{6 \sqrt{78} + 53}}{6} + \frac{7}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{6 \sqrt{78} + 53}}{6} + \frac{\sqrt{3}}{6 \sqrt[3]{6 \sqrt{78} + 53}}\right) \approx 3.1572981 -1.3051515 i\end{aligned}\]

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

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