3*( $(1-x)^{3}$+ $x^{3}$)+2x $(1-x)^{2}$=0
You asked:
Solve the equation \(3 \cdot \left({\left( 1 - x \right)}^{3} + {x}^{3}\right) + 2 \cdot {x\left( 1 - x \right)}^{2} = 0\) for the variable \(x\).
MathBot Answer:
The 4 solutions to the equation are: \[\begin{aligned}x &= \frac{1}{2} - \frac{i \sqrt{\sqrt{57} + 8}}{2} \approx 0.5 -1.9716639 i\\x &= \frac{1}{2} + \frac{i \sqrt{\sqrt{57} + 8}}{2} \approx 0.5 + 1.9716639 i\\x &= \frac{1}{2} - \frac{i \sqrt{8 - \sqrt{57}}}{2} \approx 0.5 -0.33547189 i\\x &= \frac{1}{2} + \frac{i \sqrt{8 - \sqrt{57}}}{2} \approx 0.5 + 0.33547189 i\end{aligned}\]
\(i\) is the imaginary unit, defined as \(i^2 = -1\).
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active 2 days ago